Baltasar Enrique Beferull Lozano

• Liu, Chengen; Money, Rohan Thekkemarickal; Gao, Ting; Sabbaqi, Mohammad; Beferull-Lozano, Baltasar & Isufi, Elvin (2026). Topological Kalman Filtering on Cell Complexes. IEEE Transactions on Signal Processing. ISSN 1053-587X. doi: https:/arxiv.org/abs/2605.15955. Full text in Research Archive Show summary

  Inferring latent dynamics from multivariate time-series defined over topological cell complexes is crucial for capturing the complex, higher-order interactions inherent in real-world systems such as in water, sensor, and transportation networks. However, reconstructing these latent states is challenging because the signals are coupled across higher-order topologies, while high dimensionality, nonlinear observations, and unknown structures increase the difficulty. To address this, we propose a topology-aware state space framework derived from stochastic partial differential equations on cell complexes. State evolution follows heat-like topological diffusion, with perturbations propagating along boundary operators. Under partial observability, we model observations using a cell complex convolution of latent states coupled with a nonlinear mapping. We perform recursive state estimation via an Extended Kalman Filter, simultaneously learning model parameters and uncertainties through an online Expectation-Maximization algorithm. Finally, for scenarios where only lower-order topological structure is known, e.g., nodes and edges, as in critical infrastructure networks, we introduce a heuristic cell identification algorithm to explicitly infer the second-order cell structures. Validations on synthetic and real datasets from water, sensor and transportation networks demonstrate that our approach yields reliable estimates under partial observability and successfully recovers the underlying topological structures.

• Canbolat, Abdullah; Money, Rohan Thekkemarickal & Beferull-Lozano, Baltasar (2026). Distributed online learning of higher-order cellular models. European Signal Processing Conference (EUSIPCO). Full text in Research Archive
• Moreno, Emilio Ruiz; Lopez-Ramos, Luis M. & Beferull-Lozano, Baltasar (2025). Upsampled Vector Autoregressive Processes. European Signal Processing Conference (EUSIPCO). Full text in Research Archive Show summary

  Vector autoregressive (VAR) processes are simple yet remarkably versatile discrete statistical models used to characterize the dynamics of a collection of variables. Although implicitly, any given VAR process assumes the highest rate, or resolution, at which those variables may vary. Hence, dynamic variations at finer rates are out of the explainability of such models by design. This paper proposes a new method to overcome this drawback. Specifically, it describes how to increase the resolution associated with any VAR process such that the process mean is unchanged and the forecast estimates at the rates given by the original resolution, and the long-run associated credible intervals, are closely preserved. Our experiments confirm the viability of the proposed method for multivariate time series analysis.

• Moreno, Emilio Ruiz & Beferull-Lozano, Baltasar (2025). Doubly Truncated Mode Kriging. In Altmann, Yoann & Davies, Mike (Ed.), 2025 IEEE Statistical Signal Processing Workshop (SSP). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9798331518004. p. 306–310. doi: 10.1109/ssp64130.2025.11073282. Full text in Research Archive
• Canbolat, Abdullah; Money, Rohan Thekkemarickal & Beferull-Lozano, Baltasar (2025). Cellular Autoregressive Higher-Order Models. In N.N. (Eds.), 2025 33rd European Signal Processing Conference (EUSIPCO). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9789464593624. p. 2517–2521. doi: 10.23919/eusipco63237.2025.11226689. Full text in Research Archive
• Canbolat, Abdullah; Money, Rohan Thekkemarickal & Beferull-Lozano, Baltasar (2025). Online Topology Identification of Higher-Order Cell Structures, 2025 IEEE 35th International Workshop on Machine Learning for Signal Processing (MLSP). IEEE (Institute of Electrical and Electronics Engineers). p. 1–6. doi: 10.1109/mlsp62443.2025.11204205. Full text in Research Archive
• Isufi, Elvin; Leus, Geert; Beferull-Lozano, Baltasar; Barbarossa, Sergio & Lorenzo, Paolo Di (2025). Topological signal processing and learning: Recent advances and future challenges. Signal Processing. ISSN 0165-1684. 233, p. 109930–109930. doi: 10.1016/j.sigpro.2025.109930. Full text in Research Archive
• Jaiswal, Rahul Kumar; Elnourani, Mohamed; Deshmukh, Siddharth & Beferull-Lozano, Baltasar (2025). A Data-driven Transfer Learning Method for Indoor Radio Map Estimation. IEEE Transactions on Vehicular Technology. ISSN 0018-9545. 75(3), p. 4261–4277. doi: 10.1109/tvt.2025.3609207. Full text in Research Archive Show summary

  Estimating accurate radio maps is important for various tasks in wireless communications, such as localization, resource allocation, and network planning. Due to the changes in the propagation characteristics of the wireless environments, a radio map model learned under a particular wireless environment cannot be directly used in a new wireless environment. Moreover, learning a new model for every environment requires, in general, a large amount of data and is computationally demanding. In this work, we design an effective novel data-driven transfer learning method that transfers and fine-tunes a deep neural network (DNN)-based radio map model learned from an original indoor wireless environment to other indoor environments with a certain level of similarity. Since other widely used similarity measures do not consider the wireless propagation characteristics, we design a data-driven similarity measure that predicts the mean square error (MSE) of the estimated power values and the amount of training data needed when learning a radio map in a new environment. Extensive simulations over several wireless environments of both office and cafe area environments show that the proposed method achieves savings of approximately 40-90% in sensor measurement data while maintaining similar accuracy (MSE) as a model trained without transfer learning, and outperforms state-of-the-art methods.

• Jaiswal, Rahul Kumar; Elnourani, Mohamed; Deshmukh, Siddharth & Beferull-Lozano, Baltasar (2025). Leveraging Transfer Learning for Radio Map Estimation via Mixture of Experts. IEEE Transactions on Cognitive Communications and Networking (TCCN). ISSN 2372-2045. 12, p. 846–863. doi: 10.1109/TCCN.2025.3570469. Full text in Research Archive Show summary

  This paper leverages transfer learning (TL) on a mixture of experts (MoE) model for indoor radio map estimation. The proposed MoE combines location-based and location-free experts through a gating network exploiting their complementary benefits. To estimate the radio map in a new wireless environment, the learned model of another sufficiently similar wireless environment is transferred and fine-tuned with additional data from the new wireless environment. The proposed data-driven similarity measure predicts the amount of training data needed for TL. Results demonstrate that the proposed method achieves similar accuracy, in terms of mean square error (MSE), to a model trained without TL while only requiring 5-40% of measurement data to adapt to several varying wireless environments. The test environments include both the office area and the cafe area wireless environments. As expected, the proposed MoE method outperforms both experts as well as the state-of-the-art methods, in both the presence and the absence of noise in location-based and location-free features.

• Krishnan, Joshin; Money, Rohan; Beferull-Lozano, Baltasar & Isufi, Elvin (2024). Simplicial Vector Autoregressive Models. IEEE Transactions on Signal Processing. ISSN 1053-587X. 72, p. 5454–5469. doi: 10.1109/TSP.2024.3503063. Full text in Research Archive Show summary

  The vector autoregressive (VAR) model is extensively employed for modelling dynamic processes, yet its scalability is challenged by an overwhelming growth in parameters when dealing with several hundred time series. To overcome this issue, inductive priors (e.g., data structure) can be leveraged to restrict the parameter space while still effectively modelling the time series. We present simplicial VAR models to mitigate the curse of dimensionality in VAR models, demonstrating also their utility in capturing the dynamics of time series defined over higher-order network structures such as edges and trian- gles. The proposed models use simplicial convolutional filters to facilitate parameter sharing across simplicial signals and capture structure-aware spatio-temporal dependencies among them. We also develop a joint simplicial-temporal Fourier transform to analyze the spectral characteristics of the models, depicting them as simplicial-temporal filters. We focus on streaming signals from real-world time-varying networks and develop an online algorithm for learning simplicial VAR models with a sublinear dynamic regret bound, ensuring convergence under reasonable assumptions. Through experiments on synthetic networks, water distribution networks, and collaborating agents, we demonstrate that the proposed models attain competitive signal modelling accuracy with orders of magnitude fewer parameters than VAR models.

• Nama, Ajay Nagendra; Beferull-Lozano, Baltasar; Saad, Leila Ben & Zhou, Jing (2024). Node-Variant Graph Filter Based Multi-Agent Deep Reinforcement Learning for Aligned Game and Wireless Environments. IEEE Conference on Industrial Electronics and Applications. 19. doi: 10.1109/ICIEA61579.2024.10665191. Full text in Research Archive
• Singh, Jayant; Zhou, Jing; Beferull-Lozano, Baltasar; Yan, Shijun & Khan, Shalman (2024). Haptic Teleoperation Framework for Learning Task Space Fine Manipulation Skills. IEEE Conference on Industrial Electronics and Applications. doi: 10.1109/ICIEA61579.2024.10665270. Full text in Research Archive Show summary

  This paper introduces a framework for teaching robot fine-manipulation skills by combining haptic teleoperation with Probabilistic Movement Primitives (ProMPs). Addressing the challenges of executing precise tasks such as snap-joint manipulation, our framework utilises ROS2 alongside a cartesian compliance controller for task space operation. This setup facilitates the intuitive guidance of robots by human operators, capturing the detailed movements critical for fine-manipulation tasks. Through experiments with the UR5e 6-DOF collaborative robot arm and a 3DSystems Touch haptic device, we illustrate the accurate representation and replication of the human demonstrated tasks.

• Vinod, Dinsha; Zhou, Jing; Beferull-Lozano, Baltasar & Cenkeramaddi, Linga Reddy (2024). Event-Triggered Control for a Fog Computing Platform with AI-based Inference. IEEE Xplore Digital Library. doi: 10.1109/ICIT58233.2024.10540954. Full text in Research Archive Show summary

  This paper addresses the control-theoretic approach of an autonomous fog computing platform to process the of-ftoaded mobile robot vision data for warehouse applications. The approach entails polytopic linear parameter varying (PLPV) modelling of the fog platform and the design of an event-triggered control to process the vision data within a specified time frame called service time, by auto-scaling the computing nodes. The PLPV model is developed using dynamic mobile robot vision data with image resolution and frame rate as parameters. The developed theory is experimentally validated on a mobile robot that navigates in a warehouse application environment, and the results are presented to show the efficacy of the proposed controller in meeting the service time requirements.

• Zaman, Bakht; Lopez-Ramos, Luis M. & Beferull-Lozano, Baltasar (2023). Online Joint Topology Identification and Signal Estimation From Streams With Missing Data. IEEE Transactions on Signal and Information Processing over Networks. ISSN 2373-7778. 9, p. 691–704. doi: 10.1109/TSIPN.2023.3324569. Full text in Research Archive Show summary

  Identifying the topology underlying a set of time series is useful for tasks such as prediction, denoising, and data completion. Vector autoregressive (VAR) model-based topologies capture dependencies among time series and are often inferred from observed spatio-temporal data. When data are affected by noise and/or missing samples, topology identification and signal recovery (reconstruction) tasks must be performed jointly. Additional challenges arise when i) the underlying topology is time-varying, ii) data become available sequentially, and iii) no delay is tolerated. This study proposes an online algorithm to overcome these challenges in estimating VAR model-based topologies, having constant complexity per iteration, which makes it interesting for big-data scenarios. The inexact proximal online gradient descent framework is used to derive a performance guarantee for the proposed algorithm, in the form of a dynamic regret bound. Numerical tests are also presented, showing the ability of the proposed algorithm to track time-varying topologies with missing data in an online fashion.

• Singh, Jayant; Zhou, Jing & Beferull-Lozano, Baltasar (2023). Enhancing Multi-Agent Reinforcement Learning: Set Function Approximation and Dynamic Policy. Proceedings of the Annual Conference of the IEEE Industrial Electronics Society (IECON). ISSN 1553-572X. doi: 10.1109/IECON51785.2023.10312543. Full text in Research Archive Show summary

  While Deep Learning based methods can solve complex problems by employing Neural Networks to act as powerful function approximators, they often suffer from inflexibility in terms of deployment beyond the training scenario and also include irrelevant data priors in the form of an ordered array of input values. This problem is quite evident in the field of MultiAgent Reinforcement Learning (MARL), where most research covers methods that are trained on a fixed number of agents, restricted by the fixed size of the input vector. In this paper, we argue that this is not a reasonable assumption, both in terms of the inflexible amount of environmental information and the restrictive nature of the structure of the information. We explore DeepSets and Set Transformers as two powerful set function approximators to address the problem of cardinality invariance and permutation invariance in the observation space of a reinforcement learning agent. We explain Set-Input Reinforcement Learning (SIRL) in detail and evaluate the performance of the DeepSets and Set Transformer methods through simulated experiments on a challenging multi-agent environment, that otherwise yields sub-optimal policies through traditional function approximation approaches. We demonstrate that both DeepSets and Set Transformer based encoders scale well to increasing the number of agents from training to evaluation.

• Money, Rohan Thekkemarickal; Krishnan, Joshin Parakkulangarayil; Beferull-Lozano, Baltasar & Isufi, Elvin (2023). Scalable and Privacy-Aware Online Learning of Nonlinear Structural Equation Models. IEEE Open Journal of Signal Processing. 4, p. 61–70. doi: 10.1109/OJSP.2023.3241580. Full text in Research Archive Show summary

  An online topology estimation algorithm for nonlinear structural equation models (SEM) is proposed in this paper, addressing the nonlinearity and the non-stationarity of real-world systems. The nonlinearity is modeled using kernel formulations, and the curse of dimensionality associated with the kernels is mitigated using random feature approximation. The online learning strategy uses a group-lasso-based optimization framework with a prediction-corrections technique that accounts for the model evolution. The proposed approach has three properties of interest. First, it enjoys node-separable learning, which allows for scalability in large networks. Second, it offers privacy in SEM learning by replacing the actual data with node-specific random features. Third, its performance can be characterized theoretically via a dynamic regret analysis, showing that it is possible to obtain a linear dynamic regret bound under mild assumptions. Numerical results with synthetic and real data corroborate our findings and show competitive performance w.r.t. state-of-the-art alternatives.

• Jaiswal, Rahul Kumar; Elnourani, Mohamed; Deshmukh, Siddharth & Beferull-Lozano, Baltasar (2023). Location-free Indoor Radio Map Estimation using Transfer learning, 2023 IEEE 97th Vehicular Technology Conference (VTC2023-Spring). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9798350311143. doi: 10.1109/VTC2023-Spring57618.2023.10200979. Full text in Research Archive Show summary

  Accurate estimation of radio maps is important for various applications of wireless communications, such as network planning, and resource allocation. To learn accurate radio map models, one needs to have accurate knowledge of transmitter and receiver locations. However, it is difficult to obtain accurate locations in practice, especially, in scenarios having a high degree of wireless multi-path. Alternatively, time of arrival (ToA) features, which are easier to obtain, can be employed for estimating radio maps. To this end, this paper investigates the application of transfer learning method using ToA features for estimating radio maps under indoor wireless communications. The performance is compared with the scenarios where only the locations of receivers and both ToAs and locations of receivers, are used for estimating radio maps, assuming that locations are known. Due to the changes in propagation characteristics, a radio map model learned in a specific wireless environment cannot be directly employed in a new wireless environment. To address this issue, a data-driven transfer learning method is designed that transfers and fine-tunes a deep neural network model learned for a radio map from a source wireless environment to other distinct (target) wireless environments. Our proposed method predicts the training data required in the new wireless environments using a data-driven similarity measure. Our results demonstrate that using ToA (location-free) features results in a superior performance for estimating radio maps in terms of the necessary number of sensor measurements for estimating radio maps with a good accuracy, as compared to a location-based approach, where it may be difficult to have accurate location estimations. It leads to a saving of 70-90% of the necessary sensor measurement data for a mean square error (MSE) of 0.004.

• Moreno, Emilio Ruiz & Beferull-Lozano, Baltasar (2023). An Online Multiple Kernel Parallelizable Learning Scheme. IEEE Signal Processing Letters. ISSN 1070-9908. 31, p. 121–125. doi: 10.1109/LSP.2023.3343185. Full text in Research Archive Show summary

  —The performance of reproducing kernel Hilbert space-based methods is known to be sensitive to the choice of the reproducing kernel. Choosing an adequate reproducing kernel can be challenging and computationally demanding, especially in data-rich tasks without prior information about the solution domain. In this paper, we propose a learning scheme that scalably combines several single kernel-based online methods to reduce the kernel-selection bias. The proposed learning scheme applies to any task formulated as a regularized empirical risk minimization convex problem. More specifically, our learning scheme is based on a multi-kernel learning formulation that can be applied to widen any single-kernel solution space, thus increasing the possibility of finding higher-performance solutions. In addition, it is parallelizable, allowing for the distribution of the computational load across different computing units. We show experimentally that the proposed learning scheme outperforms the combined single-kernel online methods separately in terms of the cumulative regularized least squares cost metric.

• Krishnan, Joshin Parakkulangarayil; Money, Rohan Thekkemarickal; Beferull-Lozano, Baltasar & Isufi, Elvin (2023). Simplicial Vector Autoregressive Model For Streaming Edge Flows, 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728163277. doi: 10.1109/ICASSP49357.2023.10096095. Full text in Research Archive Show summary

  Vector autoregressive (VAR) model is widely used to model time-varying processes, but it suffers from prohibitive growth of the parameters when the number of time series exceeds a few hundreds. We propose a simplicial VAR model to mitigate the curse of dimensionality of the VAR models when the time series are defined over higher-order network structures such as edges, triangles, etc. The proposed model shares parameters across the simplicial signals by leveraging the simplicial convolutional filter and captures structure-aware spatio-temporal dependencies of the time-varying processes. Targetting the streaming signals from the real-world nonstationary networks, we develop a group-lasso-based online strategy to learn the proposed model. Using traffic and water distribution networks, we demonstrate that the proposed model achieves competitive signal prediction accuracy with a significantly less number of parameters than the VAR models.

• Nama, Ajay Nagendra; Saad, Leila Ben; Beferull-Lozano, Baltasar & Zhou, Jing (2023). Neighborhood Graph Filters Based Graph Convolutional Neural Networks for Multi-Agent Deep Reinforcement Learning. In IEEE, . (Eds.), IECON 2023- 49th Annual Conference of the IEEE Industrial Electronics Society. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9798350331820. doi: 10.1109/IECON51785.2023.10311938. Full text in Research Archive Show summary

  Multi-agent deep reinforcement learning (MADRL), where a group of agents inside multi-agent systems cooperate to achieve a common goal, has been shown useful in many applications such as collaborative robots, autonomous driving or video games involving teams. In this paper, we propose two multi-agent deep reinforcement learning (MADRL) frameworks for value function factorization built by using Graph Convolutional Neural Networks (GCNN) based on neighborhood graph filters (NGFs). These MADRL frameworks are based on the paradigm of centralized training with decentralized execution (CTDE). In this work, we show that the superior stability of the NGFs as compared to standard graph filters leads also to superior performance for the MADRL algorithms. In the first MADRL framework, the NGF-based GCNN is used to predict the local q-value at each of the agents, while in the other one, the NGF-based GCNN is used to mix the local q-values to generate a global Q-value. We have compared the performance of NGF-based GCNNs over state-of-the-art graph neural networks for value function factorization in the MADRL framework for the StarCraft II and Coalition Structure Generation problems. The results show that the proposed MARL frameworks outperform the existing state-of-art architectures.

• Moreno, Emilio Ruiz; Lopez-Ramos, Luis M. & Beferull-Lozano, Baltasar (2023). A Trainable Approach to Zero-Delay Smoothing Spline Interpolation. IEEE Transactions on Signal Processing. ISSN 1053-587X. 71, p. 4317–4329. doi: 10.1109/TSP.2023.3329946. Full text in Research Archive Show summary

  The task of reconstructing smooth signals from streamed data in the form of signal samples arises in various applications. This work addresses such a task subject to a zerodelay response; that is, the smooth signal must be reconstructed sequentially as soon as a data sample is available and without having access to subsequent data. State-of-the-art approaches solve this problem by interpolating consecutive data samples using splines. Here, each interpolation step yields a piece that ensures a smooth signal reconstruction while minimizing a cost metric, typically a weighted sum between the squared residual and a derivative-based measure of smoothness. As a result, a zerodelay interpolation is achieved in exchange for an almost certainly higher cumulative cost as compared to interpolating all data samples together. This paper presents a novel approach to further reduce this cumulative cost on average. First, we formulate a zero-delay smoothing spline interpolation problem from a sequential decision-making perspective, allowing us to model the future impact of each interpolated piece on the average cumulative cost. Then, an interpolation method is proposed to exploit the temporal dependencies between the streamed data samples. Our method is assisted by a recurrent neural network and accordingly trained to reduce the accumulated cost on average over a set of example data samples collected from the same signal source generating the signal to be reconstructed. Finally, we present extensive experimental results for synthetic and real data showing how our approach outperforms the abovementioned state-of-the-art.

• Singh, Aditya; Redhu, Surender; Beferull-Lozano, Baltasar & Hegde, Rajesh M. (2023). Network-aware RF-energy harvesting for designing energy efficient IoT networks. Internet of Things: Engineering Cyber Physical Human Systems. 22. doi: 10.1016/j.iot.2023.100770. Full text in Research Archive Show summary

  Energy Harvesting plays a crucial role in improving the network lifetime of an IoT application. Radio Frequency (RF) energy is one of the most prominent ambient energy sources available that can be used for harvesting energy. Moreover, a number of dedicated RF-energy transmitters is required for sufficient energy transfer to the power deficit IoT nodes. However, the appropriate positioning of these RF-energy transmitters in the network is a challenging issue. In this context, a network-aware RF-energy transmitter positioning scheme is proposed in this work. This RFenergy transmitter deployment scheme considers different network performance parameters such as energy-hole information, node-connectivity information, and data routing information for RF-energy transmitter placement. Apart from that, the amount of RF-energy harvested is constrained to the RF-energy carried by the propagating RF-waves. Moreover, the wireless medium uncertainties result in severe attenuation of the propagating RF-waves. In this regard, a robust hybrid RF-wave propagation model is also proposed. The proposed model amalgamates different wave propagation mechanisms for signal strength prediction in the propagating RF-waves. This helps in improving the modelling accuracy of the RF-waves. The proposed model also predicts the amount of residual RF-energy available in the propagating RF-wave for harvesting. This model is also validated against the practical datasets generated from experiments. The proposed transmitter positioning scheme, along with the hybrid RF-wave propagation model, overcome the energy hole issue in the IoT networks and improves energy efficiency. Extensive simulations are conducted under various network scenarios to evaluate the energy harvesting performance of the proposed methods. It is observed that the proposed network-aware RF-energy harvesting scheme improves the network performance in terms of energy harvesting, network coverage, and the lifetime of IoT network.

• Ghari, Siavash Mollaebrahim & Beferull-Lozano, Baltasar (2023). Distributed Linear Network Operators Based on Successive Graph Shift Matrices. IEEE Transactions on Signal and Information Processing over Networks. ISSN 2373-7778. 9, p. 315–328. doi: 10.1109/TSIPN.2023.3271148. Full text in Research Archive Show summary

  In the context of graph signal processing, the existing distributed approaches for implementing linear network operators rely on the notion of graph shift matrix, which captures the local structure of the graph. Most of the existing approaches consider only a restricted set of linear network operators. However, in this paper, we focus on approximating general linear network operators as fast as possible after a finite number of local exchanges, with a negligible error. We propose a new distributed successive method based on designing a sequence of different graph shift matrices, which are optimized to approximate the desired network operator in an approximately minimal number of iterations. We also consider the robustness of the distributed computation of linear operators against graph perturbations. For this, we first analyze the effect of graph perturbations on our successive method and then, we incorporate the effect of graph perturbations in our design by proposing an online kernel-based estimator, which enables the nodes of the network to estimate the missing values caused by graph perturbations across iterations via available information received from neighbor nodes. Our numerical results demonstrate the superior performance of our methods over the existing state-of-the-art approaches.

• Money, Rohan Thekkemarickal; Krishnan, Joshin Parakkulangarayil & Beferull-Lozano, Baltasar (2023). Sparse Online Learning With Kernels Using Random Features for Estimating Nonlinear Dynamic Graphs. IEEE Transactions on Signal Processing. ISSN 1053-587X. 71, p. 2027–2042. doi: 10.1109/TSP.2023.3282068. Full text in Research Archive Show summary

  Online topology estimation of graph-connected time series is challenging in practice, particularly because the dependencies between the time series in many real-world scenarios are nonlinear. To address this challenge, we introduce a novel kernel-based algorithm for online graph topology estimation. Our proposed algorithm also performs a Fourier-based random feature approximation to tackle the curse of dimensionality associated with kernel representations. Exploiting the fact that real-world networks often exhibit sparse topologies, we propose a group-Lasso based optimization framework, which is solved using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. We provide theoretical guarantees for our algorithm and prove that it can achieve sublinear dynamic regret under certain reasonable assumptions. In experiments conducted on both real and synthetic data, our method outperforms existing state-of-the-art competitors.

• Elnourani, Mohamed; Deskmukh, Siddharth & Beferull-Lozano, Baltasar (2022). Resource Allocation for Underlay Interfering D2D Networks with Multi-antenna and Imperfect CSI. IEEE Transactions on Communications. ISSN 0090-6778. 70(9), p. 6066–6082. doi: 10.1109/TCOMM.2022.3194193. Full text in Research Archive Show summary

  Underlay Device-to-Device (D2D) communications improve the spectral efficiency by simultaneously allowing direct communication between D2D-users on the same channels as cellular users (CU). However, most related works consider perfect Channel State Information (CSI) with single-antenna transmissions and usually assign each channel to one D2D pair. In this work, we formulate an optimization problem for maximizing the aggregate rate of all D2D pairs and CUs in single and multiple antenna configurations under imperfect CSI, by optimizing channel and power resources. Our formulation guarantees probability of outage below a specified threshold and fairness in channel allocation across D2D pairs. The resulting problem is a stochastic-mixed-integer-non-convex problem, we solve it approximately by alternating between power-allocation and channel-assignment sub-problems. The stochastic objective and outage constraints are addressed by the concept of order-of-statistics in the single-antenna case and the Bernstein-type inequality in the multiple-antenna configuration. The power-allocation sub-problem is solved by exploiting a quadratic-transformation, while the channel-assignment sub-problem is solved by integer relaxation. Furthermore, two computationally efficient algorithms are proposed to approximately solve the problem in a partially decentralized manner. We also establish convergence guarantees for the different algorithms proposed in this work. Simulation results show that the proposed approach achieves higher throughput compared to the state-of-the-art alternatives.

• Singh, Jayant; Zhou, Jing; Beferull-Lozano, Baltasar & Tyapin, Ilya (2022). Learning Cooperative Multi-Agent Policies with Multi-Channel Reward Curriculum Based Q-Learning. Proceedings of the Annual Conference of the IEEE Industrial Electronics Society (IECON). ISSN 1553-572X. doi: 10.1109/IECON49645.2022.9969046. Full text in Research Archive Show summary

  Multi-Agent Reinforcement Learning (MARL) algorithms based on the Centralised Training Decentralised Execution (CTDE) approach have seen a great deal of interest in recent years. Most of the recent works focus on a specific class of environments built on the StartCraft Multi-Agent Challenge (SMAC) environment suite. However, experiments with the PettingZoo multi-particle environments show poor performance in an interesting subset of tasks. In this paper, the nature of these environments and the reward structures are analyzed. It shows that poor performance in these tasks is not due to a lack of representation power in the individual Q function or mixing functions, but rather a result of convergence to a suboptimal equilibrium of dual channel rewards and the issue of agent-reward decoupling that can be a common problem for many MARL environments. We present reward curriculum-based versions of QMIX and VDN as a solution to these problems and compare their results with the standard algorithms. The results show a clear performance gain in terms of a common cumulative reward metric.

• Jaiswal, Rahul Kumar; Deshmukh, Siddharth; Elnourani, Mohamed & Beferull-Lozano, Baltasar (2022). Transfer Learning Based Joint Resource Allocation for Underlay D2D Communications, 2022 IEEE Wireless Communications and Networking Conference (WCNC). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665442664. p. 1479–1484. doi: 10.1109/WCNC51071.2022.9771636. Full text in Research Archive Show summary

  In this paper, we investigate the application of transfer learning to train a Deep Neural Network (DNN) model for joint channel and power allocation in underlay device-todevice (D2D) communication. Based on the traditional optimization solutions, generating training dataset for scenarios with perfect channel state information (CSI) is not computationally demanding, compared to scenarios with imperfect CSI. Thus, a transfer learning-based approach can be exploited to transfer the DNN model trained for the perfect CSI scenarios to the imperfect CSI scenarios. We also consider the issue of defining the similarity between two types of resource allocation tasks. For this, we first determine the value of outage probability for which two resource allocation tasks are same, that is, for which our numerical results illustrate the minimal need of relearning from the transferred DNN model. For other values of outage probability, there is a mismatch between the two tasks and our results illustrate a more efficient relearning of the transferred DNN model. Our results show that the learning dataset required for relearning of the transferred DNN model is significantly smaller than the required training dataset for a DNN model without transfer learning.

• Saad, Leila Ben; Nama, Ajay Nagendra & Beferull-Lozano, Baltasar (2022). Neighborhood Graph Neural Networks under Random Perturbations and Quantization Errors, 2022 IEEE 23rd International Workshop on Signal Processing Advances in Wireless Communication (SPAWC). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665494557. doi: 10.1109/SPAWC51304.2022.9834020. Full text in Research Archive Show summary

  Graph convolutional neural networks (GCNNs) have emerged as a promising tool in the deep learning community to learn complex hidden relationships of data generated from non-Euclidean domains and represented as graphs. GCNNs are formed by a cascade of layers of graph filters, which replace the classical convolution operation in convolutional neural networks. These graph filters, when operated over real networks, can be subject to random perturbations due to link losses that can be caused by noise, interference and adversarial attacks. In addition, these graph filters are executed by finite-precision processors, which generate numerical quantization errors that may affect their performance. Despite the research works studying the effect of either graph perturbations or quantization in GCNNs, their robustness against both of these problems jointly is still not well investigated and understood. In this paper, we propose a quantized GCNN architecture based on neighborhood graph filters under random graph perturbations. We investigate the stability of such architecture to both random graph perturbations and quantization errors. We prove that the expected error due to quantization and random graph perturbations at the GCNN output is upper-bounded and we show how this bound can be controlled. Numerical experiments are conducted to corroborate our theoretical findings.

• Jaiswal, Rahul Kumar; Elnourani, Mohamed; Deshmukh, Siddharth & Beferull-Lozano, Baltasar (2022). Deep Transfer Learning Based Radio Map Estimation for Indoor Wireless Communications, 2022 IEEE 23rd International Workshop on Signal Processing Advances in Wireless Communication (SPAWC). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665494557. doi: 10.1109/SPAWC51304.2022.9833974. Full text in Research Archive Show summary

  This paper investigates the problem of transfer learning in radio map estimation for indoor wireless communications, which can be exploited for different applications, such as channel modelling, resource allocation, network planning, and reducing the number of necessary power measurements. Due to the nature of wireless communications, a radio map model developed under a particular environment can not be directly used in a new environment because of the changes in the propagation characteristics, thus creating a new model for every environment requires in general a large amount of data and is computationally demanding. To address these issues, we design an effective novel data-driven transfer learning procedure that transfers and fine-tunes a deep neural network (DNN)-based model for a radio map learned from an original indoor wireless environment to other different indoor wireless environments. Our method allows to predict the amount of training data needed in new indoor wireless environments when performing the operation of transfer learning using our similarity measure. Our simulation results illustrate that the proposed method achieves a saving of 60-70% in sensor measurement data and is able to adapt to a new wireless environment with a small amount of additional data.

• Elnourani, Mohamed; Deshmukh, Siddharth & Beferull-Lozano, Baltasar (2022). Resource Allocation for Underlay Interfering D2D Networks With Multiantenna and Imperfect CSI. IEEE Transactions on Communications. ISSN 0090-6778. 70(9), p. 6066–6082. doi: 10.1109/TCOMM.2022.3194193. Full text in Research Archive
• Cardenas, Juan Diego; Elnourani, Mohamed Gafar Ahmed & Beferull-Lozano, Baltasar (2022). Forecasting Aquaponic Systems Behaviour With Recurrent Neural Networks Models. Proceedings of the Northern Lights Deep Learning Workshop. 3. doi: 10.7557/18.6236. Full text in Research Archive Show summary

  Aquaponic systems provide a reliable solution to grow vegetables while cultivating fish (or other aquatic organisms) in a controlled environment. The main advantage of these systems compared with traditional soil-based agriculture and aquaculture installations is the ability to produce fish and vegetables with low water consumption. Aquaponics requires a robust control system capable of optimizing fish and plant growth while ensuring a safe operation. To support the control system, this work explores the design process of Deep Learning models based on Recurrent Neural Networks to forecast one hour of pH values in small-scale industrial Aquaponics. This implementation guides us through the machine learning life-cycle with industrial time-series data, i.e. data acquisition, pre-processing, feature engineering, architecture selection, training, and model verification.

• Money, Rohan Thekkemarickal; Krishnan, Joshin Parakkulangarayil & Beferull-Lozano, Baltasar (2022). Online Joint Nonlinear Topology Identification and Missing Data Imputation over Dynamic Graphs. In N, N (Eds.), 30th European Signal Processing Conference (EUSIPCO 2022). European Association for Signal Processing. ISSN 9789082797091. p. 687–691. doi: 10.23919/EUSIPCO55093.2022.9909681. Full text in Research Archive Show summary

  Extracting causal graph structures from multivariate time series, termed topology identification, is a fundamental problem in network science with several important applications. Topology identification is a challenging problem in real-world sensor networks, especially when the available time series are partially observed due to faulty communication links or sensor failures. The problem becomes even more challenging when the sensor dependencies are nonlinear and nonstationary. This paper proposes a kernel-based online framework using random feature approximation to jointly estimate nonlinear causal dependencies and missing data from partial observations of streaming graph-connected time series. Exploiting the fact that real-world networks often exhibit sparse topologies, we propose a group lasso-based optimization framework for topology identification, which is solved online using alternating minimization techniques. The ability of the algorithm is illustrated using several numerical experiments conducted using both synthetic and real data.

• Elnourani, Mohamed; Deshmukh, Siddharth; Beferull-Lozano, Baltasar & Romero, Daniel (2022). Robust Sum-Rate Maximization for Underlay Device-to-Device Communications on Multiple Channels. IEEE Transactions on Vehicular Technology. ISSN 0018-9545. 71(3), p. 3075–3091. doi: 10.1109/TVT.2022.3145011. Full text in Research Archive Show summary

  Most recent works in device-to-device (D2D) underlay communications focus on the optimization of either power or channel allocation to improve the spectral efficiency, and typically consider uplink and downlink separately. Further, several of them also assume perfect knowledge of channel-state-information (CSI). In this paper, we formulate a joint uplink and downlink resource allocation scheme, which assigns both power and channel resources to D2D pairs and cellular users in an underlay network scenario. The objective is to maximize the overall network rate while maintaining fairness among the D2D pairs. In addition, we also consider imperfect CSI, where we guarantee a certain outage probability to maintain the desired quality-of-service (QoS). The resulting problem is a mixed integer non-convex optimization problem and we propose both centralized and decentralized algorithms to solve it, using convex relaxation, fractional programming, and alternating optimization. In the decentralized setting, the computational load is distributed among the D2D pairs and the base station, keeping also a low communication overhead. Moreover, we also provide a theoretical convergence analysis, including also the rate of convergence to stationary points. The proposed algorithms have been experimentally tested in a simulation environment, showing their favorable performance, as compared with the state-of-the-art alternatives.

• Money, Rohan Thekkemarickal; Krishnan, Joshin Parakkulangarayil; Beferull-Lozano, Baltasar & Isufi, Elvin (2022). Online Edge Flow Imputation on Networks. IEEE Signal Processing Letters. ISSN 1070-9908. 30, p. 115–119. doi: 10.1109/LSP.2022.3221846. Full text in Research Archive Show summary

  An online algorithm for missing data imputation for networks with signals defined on the edges is presented. Leveraging the prior knowledge intrinsic to real-world networks, we propose a bi-level optimization scheme that exploits the causal dependencies and the flow conservation, respectively via (i) a sparse line graph identification strategy based on a group-Lasso and (ii) a Kalman filtering-based signal reconstruction strategy developed using simplicial complex (SC) formulation. The advantages of this first SC-based attempt for time-varying signal imputation have been demonstrated through numerical experiments using EPANET models of both synthetic and real water distribution networks.

• Lopez-Ramos, Luis M.; Roy, Kevin & Beferull-Lozano, Baltasar (2022). Explainable Nonlinear Modelling of Multiple Time Series with Invertible Neural Networks. In Sanfilippo, Filippo; Granmo, Ole-Christoffer; Yayilgan, Sule Yildirim & Bajwa, Imran Sarwar (Ed.), Intelligent Technologies and Applications: 4th International Conference, INTAP 2021, Grimstad, Norway, October 11–13, 2021, Revised Selected Papers. Springer. ISSN 9783031105241. p. 17–30. doi: 10.1007/978-3-031-10525-8_2. Full text in Research Archive Show summary

  A method for nonlinear topology identification is proposed, based on the assumption that a collection of time series are generated in two steps: i) a vector autoregressive process in a latent space, and ii) a nonlinear, component-wise, monotonically increasing observation mapping. The latter mappings are assumed invertible, and are modeled as shallow neural networks, so that their inverse can be numerically evaluated, and their parameters can be learned using a technique inspired in deep learning. Due to the function inversion, the backpropagation step is not straightforward, and this paper explains the steps needed to calculate the gradients applying implicit differentiation. Whereas the model explainability is the same as that for linear VAR processes, preliminary numerical tests show that the prediction error becomes smaller.

• Sironja, Poorva; Redhu, Surender; Hegde, Rajesh M. & Beferull-Lozano, Baltasar (2022). Cluster-based 3D-Beam Power Management in Resource-Constrained Wireless Networks, 2022 14th International Conference on COMmunication Systems & NETworkS (COMSNETS). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665421041. p. 590–594. doi: 10.1109/COMSNETS53615.2022.9668343. Full text in Research Archive Show summary

  Abstract—Various applications of wireless 5G networks demand high throughput for improving the Quality of Service. Power management of the beams plays a key role in improving the throughput in 5G-mmWave networks. However, resource constraints make beam generation a challenging issue. In this work, cluster-based 3D beam power management schemes are proposed for improving the throughput in resource-Constrained wireless networks. Firstly, the network users are divided into a number of groups. 3D beam patterns are generated from the transmitter to maximize the throughput of users based on clustering information. The proposed cluster-based beam management scheme considers a limited amount of power resources at the transmitter. Available transmit power is distributed optimally to every cluster in the network. The performance is improved further by identifying the outliers in the clusters. The tradeoff between the transmit power and users served decides the threshold on outlier detection. The performance of proposed cluster-based 3D beam patterns is evaluated under different network scenarios using numeric simulations. The proposed method shows significant improvements in terms of throughput, network coverage, average signal-to-noise ratio (SNR), and transmit power consumption. The performance of the proposed methods is also compared with the alternative schemes under power-constrained scenarios.

• Cardenas, Juan Diego; Beferull-Lozano, Baltasar; Elnourani, Mohamed & Romero, Daniel (2022). RISK-AWARE PARTICLE FILTERING FOR STATE ESTIMATION IN RECIRCULATING AQUACULTURE SYSTEMS, 2022 56th Asilomar Conference on Signals, Systems, and Computers. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665459068. p. 829–833. doi: 10.1109/IEEECONF56349.2022.10051993. Full text in Research Archive Show summary

  We design a sequential non-linear risk-aware estimator based on particle filtering to compute estimates and approximate the system state posterior distribution. For this purpose, we consider the risk given by the expected variance of the squared error between the system state and the estimate conditioned on the observations. We compare the proposed estimator with existing risk-neutral estimators in terms of error variance, mean squared error, and execution time per iteration. The comparison is carried out using a simulation of a Recirculating Aquaculture System, a case study for non-linear critical systems, where the performance in estimation for low probability events becomes an important aspect. Our simulation results demonstrate a competitive estimation performance while ensuring a lower risk. 1 1 The reader can find the code for the proposed estimators in github.com/uia-wisenet/Risk_Aware_MMSE_PF.

• Kumar, Sarang; Elnourani, Mohamed; Beferull-Lozano, Baltasar & Redhu, Surender (2022). A Deep Learning-Based Channel Aware Single Step Signal Detection in Downlink Multi-User NOMA, 2022 IEEE 96th Vehicular Technology Conference (VTC2022-Fall). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665454681. doi: 10.1109/VTC2022-Fall57202.2022.10013001. Full text in Research Archive
• Roy, Kevin; Ramos, Luis Miguel Lopez & Beferull-Lozano, Baltasar (2022). Joint Signal Estimation and Nonlinear Topology Identification from Noisy Data with Missing Entries, 2022 56th Asilomar Conference on Signals, Systems, and Computers. IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665459068. doi: 10.1109/IEEECONF56349.2022.10051968. Full text in Research Archive
• Saad, Leila Ben; Beferull-Lozano, Baltasar & Isufi, Elvin (2021). Quantization Analysis and Robust Design in Distributed Graph Filters. IEEE Transactions on Signal Processing. ISSN 1053-587X. 70, p. 643–658. doi: 10.1109/TSP.2021.3139208. Full text in Research Archive Show summary

  Distributed graph filters have recently found applications in wireless sensor networks (WSNs) to solve distributed tasks such as reaching consensus, signal denoising, and reconstruction. However, when implemented over WSNs, the graph filters should deal with network limited energy constraints as well as processing and communication capabilities.Quantization plays a fundamental role to improve the latter but its effects on distributed graph filtering are little understood. WSNs are also prone to random link losses due to noise and interference. In this instance, the filter output is affected by both the quantization error and the topological randomness error, which, if it is not properly accounted in the filter design phase, may lead to an accumulated error through the filtering iterations and significantly degrade the performance. In this paper, we analyze how quantization affects distributed graph filtering over both time-invariant and time-varying graphs. We bring insights on the quantization effects for the twomost common graph filters: the finite impulse response (FIR) and autoregressive moving average (ARMA) graph filter. Besides providing a comprehensive analysis, we devise theoretical performance guarantees on the filter performancewhen the quantization stepsize is fixed or changes dynamically over the filtering iterations. For FIR filters, we show that a dynamic quantization stepsize leads to more reduction of the quantization noise than in the fixed-stepsize quantization. For ARMAgraph filters,we showthat decreasing the quantization stepsize over the iterations reduces the quantization noise to zero at the steady-state. In addition, we propose robust filter design strategies that minimize the quantization noise for both time-invariant and time-varying networks. Numerical experiments on synthetic and two real data sets corroborate our findings and show the different trade-offs between quantization bits, filter order, and robustness to topological randomness.

• Sharan, Ravi; Deshmukh, Siddharth; Pillai, Sibi Raj B. & Beferull-Lozano, Baltasar (2021). Energy Efficient AoI Minimization in Opportunistic NOMA/OMA Broadcast Wireless Networks. IEEE Transactions on Green Communications and Networking (ITGCN). 6(2), p. 1009–1022. doi: 10.1109/TGCN.2021.3135351. Full text in Research Archive
• Elnourani, Mohamed; Deshmukh, Siddharth & Beferull-Lozano, Baltasar (2021). Distributed Resource Allocation in Underlay Multicast D2D Communications. IEEE Transactions on Communications. ISSN 0090-6778. 69(5), p. 3409–3422. doi: 10.1109/TCOMM.2021.3058374. Full text in Research Archive Show summary

  Multicast device-to-device communications operating underlay with cellular networks is a spectral efficient technique for disseminating data to nearby receivers. However, due to the critical challenge of having an intelligent interference coordination between multicast groups along with the cellular network, it is necessary to judiciously perform resource allocation for the combined network. In this work, we present a framework for a joint channel and power allocation strategy to maximize the sum rate of the combined network while guaranteeing minimum rate to individual groups and cellular users. The objective function is augmented by an austerity function that penalizes excessive assignment of low rate channels. The formulated problem is a mixed-integer-non-convex program, which requires exponential complexity to obtain the optimal solution. To tackle this, we exploit fractional programming and integer relaxation to obtain a parametric convex approximation. Based on sequential convex approximation approach, we first propose a centralized algorithm that ensures convergence to a limit point. Next, we propose a distributed algorithm in which via dual decomposition, separable sub-problems are formulated to be solved at the respective groups in cooperation with the base station. We provide convergence guarantees of the proposed solutions and demonstrate their merits by simulations, showing improvement in network throughput.

• Ghari, Siavash Mollaebrahim; Romero, Daniel & Beferull-Lozano, Baltasar (2021). Fast Decentralized Linear Functions Via Successive Graph Shift Operators. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing. ISSN 1520-6149. p. 5225–5229. doi: 10.1109/ICASSP39728.2021.9415098. Full text in Research Archive
• Saad, Leila Ben & Beferull-Lozano, Baltasar (2021). Quantization in Graph Convolutional Neural Networks, 2021 29th European Signal Processing Conference (EUSIPCO). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9789082797060. doi: 10.23919/EUSIPCO54536.2021.9615973. Full text in Research Archive
• Bhardwaj, Jyotirmoy; Krishnan, Joshin Parakkulangarayil & Beferull-Lozano, Baltasar (2021). Data-Driven Pump Scheduling for Cost Minimization in Water Networks. In NN, NN (Eds.), 2021 IEEE International Conference on Autonomous Systems (ICAS). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728172897. p. 197–201. doi: 10.1109/ICAS49788.2021.9551168. Full text in Research Archive Show summary

  Pumps consume a significant amount of energy in a water distribution network (WDN). With the emergence of dynamic energy cost, the pump scheduling as per user demand is a computationally challenging task. Computing the decision variables of pump scheduling relies over mixed integer optimization (MIO) formulations. However, MIO formulations are NP-hard in general and solving such problems is inefficient in terms of computation time and memory. Moreover, the computational complexity of solving such MIO formulations increases exponentially with the size of the WDN. As an alternative, we propose a data-driven approach to estimate the decision variables of pump scheduling using deep neural networks (DNN). We evaluate the performance of our trained DNN relative to a state-of-the-art MIO solver, and conclude that our DNN based approach can be used to minimize the pump switching and cost incurred due to dynamic energy in a given WDN with much lower complexity.

• Money, Rohan Thekkemarickal; Krishnan, Joshin Parakkulangarayil & Beferull-Lozano, Baltasar (2021). Online Non-linear Topology Identification from Graph-connected Time Series. In NN, NN (Eds.), 2021 IEEE Data Science and Learning Workshop (DSLW). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781665428255. doi: 10.1109/DSLW51110.2021.9523399. Full text in Research Archive Show summary

  Estimating the unknown causal dependencies among graph-connected time series plays an important role in many applications, such as sensor network analysis, signal processing over cyber-physical systems, and finance engineering. Inference of such causal dependencies, often know as topology identification, is not well studied for non-linear non-stationary systems, and most of the existing methods are batch-based which are not capable of handling streaming sensor signals. In this paper, we propose an online kernel-based algorithm for topology estimation of non-linear vector autoregressive time series by solving a sparse online optimization framework using the composite objective mirror descent method. Experiments conducted on real and synthetic data sets show that the proposed algorithm outperforms the state-of-the-art methods for topology estimation.

• Saad, Leila Ben; Beferull-Lozano, Baltasar & Isufi, Elvin (2021). Quantization Analysis and Robust Design for Distributed Graph Filters. IEEE Transactions on Signal Processing. ISSN 1053-587X. 70. doi: 10.1109/TSP.2021.3139208. Full text in Research Archive Show summary

  Distributed graph filters have recently found appli- cations in wireless sensor networks (WSNs) to solve distributed tasks such as reaching consensus, signal denoising, and recon- struction. However, when implemented over WSNs, the graph filters should deal with network limited energy constraints as well as processing and communication capabilities. Quantization plays a fundamental role to improve the latter but its effects on distributed graph filtering are little understood. WSNs are also prone to random link losses due to noise and interference. In this instance, the filter output is affected by both the quantization error and the topological randomness error, which, if it is not properly accounted in the filter design phase, may lead to an accumulated error through the filtering iterations and significantly degrade the performance. In this paper, we analyze how quantization affects distributed graph filtering over both time-invariant and time-varying graphs. We bring insights on the quantization effects for the two most common graph filters: the finite impulse response (FIR) and autoregressive moving average (ARMA) graph filter. Besides providing a comprehensive anal- ysis, we devise theoretical performance guarantees on the filter performance when the quantization stepsize is fixed or changes dynamically over the filtering iterations. For FIR filters, we show that a dynamic quantization stepsize leads to more control on the quantization noise than the fixed-stepsize quantization. For ARMA graph filters, we show that decreasing the quantization stepsize over the iterations reduces the quantization noise to zero at the steady-state. In addition, we propose robust filter design strategies that minimize the quantization noise for both time- invariant and time-varying networks. Numerical experiments on synthetic and two real data sets corroborate our findings and show the different trade-offs between quantization bits, filter order, and robustness to topological randomness.

• Money, Rohan Thekkemarickal; Krishnan, Joshin Parakkulangarayil & Beferull-Lozano, Baltasar (2021). Random Feature Approximation for Online Nonlinear Graph Topology Identification. Machine Learning for Signal Processing. ISSN 1551-2541. doi: 10.1109/MLSP52302.2021.9596512. Full text in Research Archive Show summary

  Online topology estimation of graph-connected time series is challenging, especially since the causal dependencies in many real-world networks are nonlinear. In this paper, we propose a kernel-based algorithm for graph topology estimation. The algorithm uses a Fourier-based Random feature approximation to tackle the curse of dimensionality associated with the kernel representations. Exploiting the fact that the real-world networks often exhibit sparse topologies, we propose a group lasso based optimization framework, which is solve using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. The experiments conducted on real and synthetic data show that the proposed method outperforms its competitors.

• Moreno, Emilio Ruiz & Beferull-Lozano, Baltasar (2021). Tracking of Quantized Signals Based on Online Kernel Regression. Machine Learning for Signal Processing. ISSN 1551-2541. doi: 10.1109/MLSP52302.2021.9596115. Full text in Research Archive Show summary

  Kernel-based approaches have achieved noticeable success as non-parametric regression methods under the framework of stochastic optimization. However, most of the kernel-based methods in the literature are not suitable to track sequentially streamed quantized data samples from dynamic environments. This shortcoming occurs mainly for two reasons: first, their poor versatility in tracking variables that may change unpredictably over time, primarily because of their lack of flexibility when choosing a functional cost that best suits the associated regression problem; second, their indifference to the smoothness of the underlying physical signal generating those samples. This work introduces a novel algorithm constituted by an online regression problem that accounts for these two drawbacks and a stochastic proximal method that exploits its structure. In addition, we provide tracking guarantees by analyzing the dynamic regret of our algorithm. Finally, we present some experimental results that support our theoretical analysis and show that our algorithm has a favorable performance compared to the state-of-the-art.

• Ghari, Siavash Mollaebrahim & Beferull-Lozano, Baltasar (2021). Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection. IEEE Transactions on Signal Processing. ISSN 1053-587X. 69, p. 2056–2069. doi: 10.1109/TSP.2021.3066787. Full text in Research Archive
• Redhu, Surender; Singh, Amrendra P.; Hedge, Rajesh M & Beferull-Lozano, Baltasar (2021). A Cluster based Sensor-Selection Scheme for Energy-Efficient Agriculture Sensor Networks, 2021 IEEE 18th Annual Consumer Communications & Networking Conference (CCNC). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728197944. doi: 10.1109/CCNC49032.2021.9369595. Full text in Research Archive
• Bhardwaj, Jyotirmoy; Krishnan, Joshin Parakkulangarayil; Marin, Diego F. Larios; Beferull-Lozano, Baltasar; Cenkeramaddi, Linga Reddy & Harman, Christopher Peter (2021). Cyber-Physical Systems for Smart Water Networks: A Review. IEEE Sensors Journal. ISSN 1530-437X. 21(23), p. 26447–26469. doi: 10.1109/JSEN.2021.3121506. Full text in Research Archive Show summary

  There is a growing demand to equip Smart Water Networks (SWN) with advanced sensing and computation capabilities in order to detect anomalies and apply autonomous event-triggered control. Cyber-Physical Systems (CPSs) have emerged as an important research area capable of intelligently sensing the state of SWN and reacting autonomously in scenarios of unexpected crisis development. Through computational algorithms, CPSs can integrate physical components of SWN, such as sensors and actuators, and provide technological frameworks for data analytics, pertinent decision making, and control. The development of CPSs in SWN requires the collaboration of diverse scientific disciplines such as civil, hydraulics, electronics, environment, computer science, optimization, communication, and control theory. For efficient and successful deployment of CPS in SWN, there is a need for a common methodology in terms of design approaches that can involve various scientific disciplines. This paper reviews the state of the art, challenges, and opportunities for CPSs, that could be explored to design the intelligent sensing, communication, and control capabilities of CPS for SWN. In addition, we look at the challenges and solutions in developing a computational framework from the perspectives of machine learning, optimization, and control theory for SWN.

• Elnourani, Mohamed; Deshmukh, Siddharth; Beferull-Lozano, Baltasar & Romero, Daniel (2020). Robust Transmit Beamforming for Underlay D2D Communications on Multiple Channels, 2020 IEEE 21st International Workshop on Signal Processing Advances in Wireless Communications (SPAWC). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728154787. doi: 10.1109/SPAWC48557.2020.9154329. Full text in Research Archive
• Elnourani, Mohamed; Deshmukh, Siddharth & Beferull-Lozano, Baltasar (2020). Reliable Underlay D2D Communications over Multiple Transmit Antenna Framework, ICC 2020 - 2020 IEEE International Conference on Communications (ICC). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728150895. doi: 10.1109/ICC40277.2020.9149079. Full text in Research Archive Show summary

  Robust beamforming is an efficient technique to guarantee the desired receiver performance in the presence of erroneous channel state information (CSI). However, the application of robust beamforming in underlay device-to-device (D2D) communication still requires further investigation. In this paper, we investigate resource allocation problem for underlay D2D communications by considering multiple antennas at the base station (BS) and at the transmitters of D2D pairs. The proposed design problem aims at maximizing the aggregate rate of all D2D pairs and cellular users (CUs) in downlink spectrum. In addition, our objective is augmented to achieve a fair allocation of resources across the D2D pairs. Further, assuming elliptically bounded CSI errors, the formulation ensures maintaining signal to interference plus noise ratio (SINR) above a specified threshold. The derived optimization problem results in a mixed integer non-convex problem and requires exponential complexity to obtain the optimal solution. We perform a semi-definite relaxation (SDR) to handle the stochastic SINR constraints by using the S-Lemma, obtaining a number of linear matrix inequalities. The non-convexity is addressed by introducing slack variables and performing a quadratic transformation to obtain sub-optimal beamformers via alternating optimization. The solution for channel assignments to D2D pairs is obtained by convex relaxation of the integer constraints. Finally, we demonstrate the merit of the proposed approach by simulations in which we observe higher and more robust network throughput, as compared to previous state-of-the-art.

• Sharma, Sanjeev; Deka, Kuntal & Beferull-Lozano, Baltasar (2020). Low-complexity detection for uplink massive MIMO SCMA systems. IET Communications. ISSN 1751-8628. 15(1), p. 51–59. doi: 10.1049/cmu2.12057. Full text in Research Archive
• Zaman, Bakht; Lopez-Ramos, Luis M. & Beferull-Lozano, Baltasar (2020). Dynamic Regret Analysis for Online Tracking of Time-varying Structural Equation Model Topologies. In Li, Zhengguo (Eds.), Proceedings of the 15th IEEE Conference on Industrial Electronics and Applications(ICIEA 2020). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728151687. p. 939–944. doi: 10.1109/ICIEA48937.2020.9248365. Full text in Research Archive Show summary

  Identifying dependencies among variables in a complex system is an important problem in network science. Structural equation models (SEM) have been used widely in many fields for topology inference, because they are tractable and incorporate exogenous influences in the model. Topology identification based on static SEM is useful in stationary environments; however, in many applications a time-varying underlying topology is sought. This paper presents an online algorithm to track sparse time-varying topologies in dynamic environments and most importantly, performs a detailed analysis on the performance guarantees. The tracking capability is characterized in terms of a bound on the dynamic regret of the proposed algorithm. Numerical tests show that the proposed algorithm can track changes under different models of time-varying topologies.

• Ghari, Siavash Mollaebrahim; Beferull-Lozano, Baltasar & Moreno, Emilio Ruiz (2020). Decentralized Subspace Projection for Asymmetric Sensor Networks. IEEE Vehicular Technology Conference (VTC). ISSN 1090-3038. doi: 10.1109/VTC2020-Fall49728.2020.9348681. Full text in Research Archive
• Deka, Kuntal; Priyadarsini, Minerva; Sharma, Sanjeev & Beferull-Lozano, Baltasar (2020). Design of SCMA Codebooks using Differential Evolution. IEEE/CIC International Conference on Communications in China - Workshops (CIC/ICCC). ISSN 2474-9133. doi: 10.1109/ICCWorkshops49005.2020.9145202. Full text in Research Archive
• Saad, Leila Ben & Beferull-Lozano, Baltasar (2020). Accurate Graph Filtering in Wireless Sensor Networks. IEEE Internet of Things Journal. ISSN 2327-4662. 7(12). doi: 10.1109/JIOT.2020.3010610. Full text in Research Archive Show summary

  Wireless sensor networks (WSNs) are considered as a major technology enabling the Internet-of-Things (IoT) paradigm. The recent emerging graph signal processing field can also contribute to enabling the IoT by providing key tools, such as graph filters (GFs), for processing the data associated with the sensor devices. GFs can be performed over WSNs in a distributed manner by means of a certain number of communication exchanges among the nodes. But, WSNs are often affected by interferences and noise, which leads to view these networks as directed, random and time-varying graph topologies. Most of the existing works neglect this problem by considering an unrealistic assumption that claims the same probability of link activation in both directions when sending a packet between two neighboring nodes. This work focuses on the problem of operating graph filtering in random asymmetric WSNs. We show first that graph filtering with finite impulse response GFs (node-invariant and node-variant) requires having equal connectivity probabilities for all the links in order to have an unbiased filtering, which cannot be achieved in practice in random WSNs. After this, we characterize the graph filtering error and present an efficient strategy to conduct graph filtering tasks over random WSNs with node-variant GFs by maximizing accuracy, that is, ensuring a small bias-variance tradeoff. In order to enforce the desired accuracy, we optimize the filter coefficients and design a cross-layer distributed scheduling algorithm (CDSA) at the MAC layer. Extensive numerical experiments are presented to show the efficiency of the proposed solution as well as the CDSA for the denoising application.

• Elnourani, Mohamed; Deshmukh, Siddharth & Beferull-Lozano, Baltasar (2020). Reliable Multicast D2D Communication over Multiple Channels in Underlay Cellular Networks. IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications workshops. ISSN 2166-9570. 2020. doi: 10.1109/PIMRC48278.2020.9217293. Full text in Research Archive Show summary

  Multicast device-to-device (D2D) communications operating underlay with cellular networks is a spectral efficient technique for disseminating data to the nearby receivers. However, due to critical challenges such as, mitigating mutual interference and unavailability of perfect channel state information (CSI), the resource allocation to multicast groups needs significant attention. In this work, we present a framework for joint channel assignment and power allocation strategy to maximize the sum rate of the combined network. The proposed framework allows access of multiple channels to the multicast groups, thus improving the achievable rate of the individual groups. Furthermore, fairness in allocating resources to the multicast groups is also ensured by augmenting the objective with a penalty function. In addition, considering imperfect CSI, the framework guarantees to provide rate above a specified outage for all the users. The formulated problem is a mixed integer nonconvex program which requires exponential complexity to obtain the optimal solution. To tackle this, we first introduce auxiliary variables to decouple the original problem into smaller power allocation problems and a channel assignment problem. Next, with the aid of fractional programming via a quadratic transformation, we obtain an efficient power allocation solution by alternating optimization. The solution for channel assignment is obtained by convex relaxation of integer constraints. Finally, we demonstrate the merit of the proposed approach by simulations, showing a higher and a more robust network throughput. Index Terms—D2D multicast communications, resource allocation, imperfect CSI, fractional programming.

• Zaman, Bakht; Ramos, Luis Miguel Lopez; Romero, Daniel & Beferull-Lozano, Baltasar (2020). Online Topology Identification From Vector Autoregressive Time Series. IEEE Transactions on Signal Processing. ISSN 1053-587X. 69, p. 220–225. doi: 10.1109/TSP.2020.3042940. Full text in Research Archive Show summary

  Causality graphs are routinely estimated in social sciences, natural sciences, and engineering due to their capacity to efficiently represent the spatiotemporal structure of multi-variate data sets in a format amenable for human interpretation, forecasting, and anomaly detection. A popular approach to mathematically formalize causality is based on vector autoregressive (VAR) models and constitutes an alternative to the well-known, yet usually intractable, Granger causality. Relying on such a VAR causality notion, this paper develops two algorithms with complementary benefits to track time-varying causality graphs in an online fashion. Their constant complexity per update also renders these algorithms appealing for big-data scenarios. Despite using data sequentially, both algorithms are shown to asymptotically attain the same average performance as a batch estimator which uses the entire data set at once. To this end, sublinear (static) regret bounds are established. Performance is also characterized in time-varying setups by means of dynamic regret analysis. Numerical results with real and synthetic data further support the merits of the proposed algorithms in static and dynamic scenarios.

• Ramos, Luis Miguel Lopez; Teganya, Yves; Beferull-Lozano, Baltasar & Kim, Seung-Jun (2020). Channel Gain Cartography via Mixture of Experts. In NN, NN (Eds.), 2020 IEEE Global Communications Conference (GLOBECOM). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781728182988. doi: 10.1109/GLOBECOM42002.2020.9322198. Full text in Research Archive Show summary

  In order to estimate the channel gain (CG) between the locations of an arbitrary transceiver pair across a geographic area of interest, CG maps can be constructed from spatially distributed sensor measurements. Most approaches to build such spectrum maps are location-based, meaning that the input variable to the estimating function is a pair of spatial locations. The performance of such maps depends critically on the ability of the sensors to determine their positions, which may be drastically impaired if the positioning pilot signals are affected by multipath channels. An alternative location-free approach was recently proposed for spectrum power maps, where the input variable to the maps consists of features extracted from the positioning signals, instead of location estimates. The location-based and the location-free approaches have complementary merits. In this work, apart from adapting the location-free features for the CG maps, a method that can combine both approaches is proposed in a mixture-of-experts framework.

• Romero, Daniel; Ghari, Siavash Mollaebrahim; Beferull-Lozano, Baltasar & Marco, Cesar Asensio (2020). Fast Graph Filters for Decentralized Subspace Projection. IEEE Transactions on Signal Processing. ISSN 1053-587X. 69. doi: 10.1109/TSP.2020.3038528. Full text in Research Archive Show summary

  A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that asymptotically converges to the desired projection. In contrast, the present paper develops methods that produce these projections in a finite and approximately minimal number of iterations. Building upon tools from graph signal processing, the problem is cast as the design of a graph filter which, in turn, is reduced to the design of a suitable graph shift operator. Exploiting the eigenstructure of the projection and shift matrices leads to an objective whose minimization yields approximately minimum-order graph filters. To cope with the fact that this problem is not convex, the present work introduces a novel convex relaxation of the number of distinct eigenvalues of a matrix based on the nuclear norm of a Kronecker difference. To tackle the case where there exists no graph filter capable of implementing a certain subspace projection with a given network topology, a second optimization criterion is presented to approximate the desired projection while trading the number of iterations for approximation error. Two algorithms are proposed to optimize the aforementioned criteria based on the alternating-direction method of multipliers. An exhaustive simulation study demonstrates that the obtained filters can effectively obtain subspace projections markedly faster than existing algorithms.

• Jha, Ajit; Subedi, Dipendra; Løvsland, Per-Ove; Tyapin, Ilya; Cenkeramaddi, Linga Reddy & Beferull-Lozano, Baltasar [Show all 7 contributors for this article] (2020). Autonomous mooring towards autonomous maritime navigation and offshore operations, 15th IEEE Conference on Industrial Electronics and Applications. Institute of Electrical and Electronics Engineers (IEEE). ISSN 9781728151687. p. 1171–1175. doi: 10.1109/ICIEA48937.2020.9248169. Full text in Research Archive Show summary

  Bollard is a vital component of mooring system. It is the anchor point for mooring ropes to be fixed in order to secure the vessel or ship. An algorithm that translates the segmented mask of bollard output from masked R-CNN along with bounding box and associated class probability to its corresponding edge coordinate and finally to the single reference point for efficient detection and classification of bollard towards autonomous mooring is presented. At first stage, Mask R-CNN framework is trained with custom built bollard. The model obtained from the training is inferred with real data resulting in instance segment of bollard. The segmented mask obtained contains relatively large amount of the data points representing the whole area of bollard, which typically is not desirable. In order to precisely localize the bollard with one reference co-ordinate, the proposed algorithm is applied to segmented mask. Firstly, it translates the segmented mask to only four co-ordinate points, where each point correspond to the edge of bollard. Further, from the edges, the reference point is estimated. This causes significant reduction in point of interest (POI) and has potential to reduce the error encountered during pose estimation of the bollard in 3D thus making the autonomous mooring more precise and accurate.

• Lopez-Ramos, Luis M. & Beferull-Lozano, Baltasar (2020). Online Hyperparameter Search Interleaved with Proximal Parameter Updates, 28th European Signal Processing Conference (EUSIPCO 2020). European Signal Processing Conference. ISSN 9789082797053. p. 2085–2089. doi: 10.23919/Eusipco47968.2020.9287537. Full text in Research Archive Show summary

  There is a clear need for efficient hyperparameter optimization (HO) algorithms for statistical learning, since commonly applied search methods (such as grid search with N-fold cross-validation) are inefficient and/or approximate. Previously existing gradient-based HO algorithms that rely on the smoothness of the cost function cannot be applied in problems such as Lasso regression. In this contribution, we develop a HO method that relies on the structure of proximal gradient methods and does not require a smooth cost function. Such a method is applied to Leave-one-out (LOO)-validated Lasso and Group Lasso, and an online variant is proposed. Numerical experiments corroborate the convergence of the proposed methods to stationary points of the LOO validation error curve, and the improved efficiency and stability of the online algorithm

• Frøytlog, Anders; Haglund, Magne Arild; Cenkeramaddi, Linga Reddy; Jordbru, Thomas; Kjellby, Rolf Arne & Beferull-Lozano, Baltasar (2019). Design and implementation of a long-range low-power wake-up radio for IoT devices. In N, N (Eds.), 2019 IEEE 5th World Forum on Internet of Things (WF-IoT). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781538649800. doi: 10.1109/WF-IoT.2019.8767353. Full text in Research Archive
• Saad, Leila Ben & Beferull-Lozano, Baltasar (2019). Graph Filtering of Time-Varying Signals over Asymmetric Wireless Sensor Networks, 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781538665282. doi: 10.1109/SPAWC.2019.8815521. Full text in Research Archive
• Kjellby, Rolf Arne; Cenkeramaddi, Linga Reddy; Frøytlog, Anders; Beferull-Lozano, Baltasar; Soumya, J. & Bhange, Meghana (2019). Long-range & Self-powered IoT Devices for Agriculture & Aquaponics Based on Multi-hop Topology. In N, N (Eds.), 2019 IEEE 5th World Forum on Internet of Things (WF-IoT). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781538649800. doi: 10.1109/WF-IoT.2019.8767196. Full text in Research Archive
• Elnourani, Mohamed; Beferull-Lozano, Baltasar; Romero, Daniel & Deshmukh, Siddharth (2019). Reliable Underlay Device-to-Device Communications on Multiple Channels, 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9781538665282. doi: 10.1109/SPAWC.2019.8815544. Full text in Research Archive
• Teganya, Yves; Romero, Daniel; Lopez-Ramos, Luis M. & Beferull-Lozano, Baltasar (2019). Location-free Spectrum Cartography. IEEE Transactions on Signal Processing. ISSN 1053-587X. 67(15), p. 4013–4026. doi: 10.1109/TSP.2019.2923151. Full text in Research Archive Show summary

  Spectrum cartography constructs maps of metrics such as channel gain or received signal power across a geographic area of interest using spatially distributed sensor measurements. Applications of these maps include network planning, interference coordination, power control, localization, and cognitive radios to name a few. Since existing spectrum cartography techniques require accurate estimates of the sensor locations, their performance is drastically impaired by multipath affecting the positioning pilot signals. This phenomenon occurs especially in indoor or dense urban scenarios. To overcome such a limitation, this paper introduces a novel paradigm for spectrum cartography, where estimation of spectral maps relies on features of these positioning signals rather than on location estimates. Specific learning algorithms are built on this approach and offer a markedly improved estimation performance than those of the existing approaches relying on localization, as demonstrated by simulation studies in indoor scenarios.

• Ghari, Siavash Mollaebrahim; Romero, Daniel & Beferull-Lozano, Baltasar (2019). Fast Decentralized Linear Functions via Successive Graph Shift Operators. arXiv.org. ISSN 2331-8422. Full text in Research Archive Show summary

  We study decentralized designing of the graph shift operators to implement linear transformations between graph signals. Since this operator captures the local structure of the graph, the proposed method of this paper gives rise to decentralized linear network operators. Unfortunately, existing decentralized approaches either consider some special instances of linear transformations or confine themselves to some known graph shift operators reduced family of the designing linear transformations task. To remedy these limitations, this paper develops a framework for computing a wide class of linear transformations in a decentralized fashion by relying on the notion of graph shift operator. To this end, a set of successive graph shift operators is implemented to compute linear transformations in a small number of iterations (as fast as possible).

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• Singh, Jayant; Zhou, Jing & Beferull-Lozano, Baltasar (2023). Enhancing Multi-Agent Reinforcement Learning: Set Function Approximation and Dynamic Policy Adaptation. Full text in Research Archive

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• Beferull-Lozano, Baltasar (2026). SURE-AI Centre for Sustainable, Risk-averse and Ethical AI. Progress, status and outlook. Full text in Research Archive Show summary

  Status update presentation of the SURE-AI Centre to the RCN Portfolio Board for Enabling Technologies

• Beferull-Lozano, Baltasar (2026). SURE-AI Centre for Sustainable, Risk-averse and Ethical AI. Full text in Research Archive Show summary

  Short presentation of SURE-AI Centre for Sustainable, Risk-averse and Ethical AI

• Beferull-Lozano, Baltasar (2026). SURE-AI Centre for Sustainable, Risk-averse and Ethical AI. Full text in Research Archive Show summary

  Presentation of the SURE-AI Centre for Sustainable, Risk-averse and Ethical AI and possibilities for collaboration

• Gancia, Gino; Mittal, Shivika; Nunno, Giulia Di; Castellacci, Fulvio & Beferull-Lozano, Baltasar (2026). SURE-AI@STAR Workshop on the Environmental Cost of AI. doi: https:/www.mn.uio.no/math/english/research/groups/risk-stochastics/events/seminars/SURE-AI@STARWorkshop-CostAI.html. Full text in Research Archive
• Beferull-Lozano, Baltasar (2025). Presentation of Norwegian centre for Sustainable, Risk-averse and Ethical AI. Full text in Research Archive Show summary

  Presentation of Norwegian centre for Sustainable, Risk-averse and Ethical AI at the CICERO staff seminar

• Beferull-Lozano, Baltasar (2025). SURE-AI Centre for Sustainable, Risk-averse and Ethical AI. Full text in Research Archive Show summary

  Presentation of SURE-AI Centre for Sustainable, Risk-averse and Ethical AI

• Ruiz, Emilio; Kousias, Konstantinos; Kumar, Shravan; Tilleman, Myrthe; Beferull-Lozano, Baltasar & Alay, Özgü [Show all 8 contributors for this article] (2025). On the limits of trajectory prediction for hand movement trajectories with motion-capture sensors. Full text in Research Archive
• Halnes, Geir; Javaid, Anam; Solvang, Michael; Nichele, Stefano; Riegler, Michael & Singstad, Bjørn-Jostein [Show all 82 contributors for this article] (2025). Proceedings of NORA’s annual conference 2025. Nordic Machine Intelligence (NMI). 5(3), p. 1–14. doi: 10.5617/nmi.12551. Full text in Research Archive
• Money, Rohan; Krishnan, Joshin & Beferull-Lozano, Baltasar (2024). Limited Data Forecasting of Financial Time-series using Graph-based Class Dynamics. doi: 10.23919/EUSIPCO63174.2024.10714981. Full text in Research Archive
• Money, Rohan; Sabbaqi, Mohammad; Krishnan, Joshin & Beferull-Lozano, Baltasar (2024). Kalman Filtering for Simplicial Processes. doi: 10.1109/IEEECONF60004.2024.10942943. Full text in Research Archive
• Dominguez-Cid, Samuel; Krishnan, Joshin; Money, Rohan & Beferull-Lozano, Baltasar (2024). Graph-Vector Auto-regressive Model for Lithium-Ion Cell Capacity Estimation. doi: 10.1109/MLSP58920.2024.10734722. Full text in Research Archive
• Money, Rohan; Krishnan, Joshin; Beferull-Lozano, Baltasar & Isufi, Elvin (2024). Evolution Backcasting of Edge Flows from Partial Observations using Simplicial Vector Autoregressive Models. doi: 10.1109/ICASSP48485.2024.10448180. Full text in Research Archive
• Jaiswal, Rahul Kumar; Elnourani, Mohamed; Deshmukh, Siddharth & Beferull-Lozano, Baltasar (2023). Location-free Indoor Radio Map Estimation using Transfer learning. Full text in Research Archive
• Cardenas-Cartagena, Juan; Elnourani, Mohamed; Beferull-Lozano, Baltasar & Romero, Daniel (2022). Risk-Aware Particle-Filtering for State Estimation in Recirculating Aquaculture Systems. Full text in Research Archive
• Ghari, Siavash Mollaebrahim & Beferull-Lozano, Baltasar (2022). Erratum: Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection (IEEE Trans. Signal Process. (2021) 69 (2056-2069) DOI: 10.1109/TSP.2021.3066787). IEEE Transactions on Signal Processing. ISSN 1053-587X. 70, p. 2842–2843. doi: 10.1109/TSP.2022.3176492. Full text in Research Archive
• Cardenas, Juan Diego; Beferull-Lozano, Baltasar; Elnourani, Mohamed & Romero, Daniel (2022). RISK-AWARE PARTICLE FILTERING FOR STATE ESTIMATION IN RECIRCULATING AQUACULTURE SYSTEMS. Full text in Research Archive
• Lopez-Ramos, Luis M. & Beferull-Lozano, Baltasar (2021). Online Hyperparameter Search Interleaved with Proximal Parameter Updates. Full text in Research Archive
• Jha, Ajit; Subedi, Dipendra; Løvsland, Per-Ove; Tyapin, Ilya; Cenkeramaddi, Linga Reddy & Beferull-Lozano, Baltasar [Show all 7 contributors for this article] (2020). Autonomous mooring towards autonomous maritime navigation and offshore operations. Full text in Research Archive
• Liltved, Helge & Beferull-Lozano, Baltasar (2020). Hydroponic systems for crop growth. Full text in Research Archive
• Frøytlog, Anders; Haglund, Magne Arild; Cenkeramaddi, Linga Reddy & Beferull-Lozano, Baltasar (2019). Design and implementation of a long-range low-power wake-up radio and customized DC-MAC protocol for LoRaWAN. Full text in Research Archive
• Idsøe, Henning; Cenkeramaddi, Linga Reddy; J, Soumya & Beferull-Lozano, Baltasar (2019). Phase-noise Impact on the Performance of mmWave-RADARs. Full text in Research Archive
• Zaman, Bakht; Lopez-Ramos, Luis M.; Romero, Daniel & Beferull-Lozano, Baltasar (2019). Online Topology Identification from Vector Autoregressive Time Series. Full text in Research Archive Show summary

  Due to their capacity to condense the spatiotemporal structure of a data set in a format amenable for human inter-pretation, forecasting, and anomaly detection, causality graphsare routinely estimated in social sciences, natural sciences, andengineering. A popular approach to mathematically formalizecausality is based on vector autoregressive (VAR) models, whichconstitutes an alternative to the well-known but usually in-tractable Granger causality. Relying on such a VAR causalitynotion, this paper develops two algorithms with complementarybenefits to track time-varying causality graphs in an onlinefashion. Despite using data in a sequential fashion, both al-gorithms are shown to asymptotically attain the same averageperformance as a batch estimator with all data available atonce. Moreover, their constant complexity per update rendersthese algorithms appealing for big-data scenarios. Theoreticaland experimental performance analysis support the merits ofthe proposed algorithms. Remarkably, no probabilistic modelsor stationarity assumptions need to be introduced, which endows the developed algorithms with considerable generality.

• Saad, Leila Ben & Beferull-Lozano, Baltasar (2019). Graph Filtering of Time-Varying Signals over Random Asymmetric Wireless Sensor Networks. Full text in Research Archive
• Moreno, Emilio Ruiz; Konstantinos, Slavakis, & Beferull-Lozano, Baltasar (2026). [2609.16472] Online Gradient Computation for Warping Gaussian Process Transformations. arxiv.org. Full text in Research Archive Show summary

  Warped Gaussian processes (GPs) handle non-Gaussian observations by mapping them into a latent standard GP via a parametric transformation called warping. Existing online variants either optimize the warping parameters periodically rather than sequentially, or sacrifice analytical tractability and computational efficiency for higher model expressivity. In this paper, we avoid these compromises. To achieve this, we first show that the gradient of the instantaneous negative log-likelihood of a warped GP admits an exact recursive computation. Based on this result, we propose a novel online method for warped GPs that jointly updates the latent GP moments and optimizes the warping parameters. Finally, we validate our method on an existing benchmark adapted to an online formulation.

• Elnourani, Mohamed; Beferull-Lozano, Baltasar & Romero, Daniel (2020). Non-convex Optimization for Resource Allocation in Wireless Device-to-Device Communications. Universitetet i Agder. ISSN 9788271179953. Full text in Research Archive Show summary

  Device-to-device (D2D) communication is considered one of the key frameworks to provide suitable solutions for the exponentially increasing data tra c in mobile telecommunications. In this PhD Thesis, we focus on the resource allocation for underlay D2D communications which often results in a non-convex optimization problem that is computationally demanding. We have also reviewed many of the works on D2D underlay communications and identi ed some of the limitations that were not handled previously, which has motivated our works in this Thesis. Our rst works focus on the joint power allocation and channel assignment problem in the D2D underlay communication scenario for a unicast single-input and single-output (SISO) cellular network in either uplink or downlink spectrums. These works also consider several degrees of uncertainty in the channel state information (CSI), and propose suitable measures to guarantee the quality of service (QoS) and reliability under those conditions. Moreover, we also present a few algorithms that can be used to jointly assign uplink and downlink spectrum to D2D pairs. We also provide methods to decentralize those algorithms with convergence guarantees and analyze their computational complexity. We also consider both cases with no interference among D2D pairs and cases with interference among D2D pairs. Additionally, we propose the formulation of an optimization objective function that combines the network rate with a penalty function that penalizes unfair channel allocations where most of the channels are assigned to only a few D2D pairs. The next contributions of this Thesis focus on extending the previous works to cellular networks with multiple-input and multiple-output (MIMO) capabilities and networks with D2D multicast groups. We also present several methods to accommodate various degrees of uncertainty in the CSI and also guarantee di erent measures of QoS and reliability. All our algorithms are evaluated extensively through extensive numerical experiments using the Matlab simulation environment. All of these results show favorable performance, as compared to the existing state-of-the-art alternatives.

• Teganya, Yves; Romero, Daniel & Beferull-Lozano, Baltasar (2020). Machine Learning Tools for Radio Map Estimation in Fading-Impaired Channels. Universitetet i Agder. ISSN 9788271179991. Full text in Research Archive Show summary

  In spectrum cartography, also known as radio map estimation, one constructs maps that provide the value of a given channel metric such as as the received power, power spectral density (PSD), electromagnetic absorption, or channel-gain for every spatial location in the geographic area of interest. The main idea is to deploy sensors and measure the target channel metric at a set of locations and interpolate or extrapolate the measurements. Radio maps nd a myriad of applications in wireless communications such as network planning, interference coordination, power control, spectrum management, resource allocation, handoff optimization, dynamic spectrum access, and cognitive radio. More recently, radio maps have been widely recognized as an enabling technology for unmanned aerial vehicle (UAV) communications because they allow autonomous UAVs to account for communication constraints when planning a mission. Additional use cases include radio tomography and source localization.

• Zaman, Bakht; Beferull-Lozano, Baltasar; Romero, Daniel & Lopez-Ramos, Luis M. (2020). Online Machine Learning for Graph Topology Identification from Multiple Time Series. Universitetet i Agder. ISSN 9788284270005. Full text in Research Archive Show summary

  High dimensional time series data are observed in many complex systems. In networked data, some of the time series are influenced by other time series. Identifying these relations encoded in a graph structure or topology among the time series is of paramount interest in certain applications since the identified structure can provide insights about the underlying system and can assist in inference tasks. In practice, the underlying topology is usually sparse, that is, not all the participating time series in influence each other. The goal of this dissertation pertains to study the problem of sparse topology identification under various settings. Topology identification from time series is a challenging task. The first major challenge in topology identification is that the assumption of static topology does not hold always in practice since most of the practical systems are evolving with time. For instance, in econometrics, social networks, etc., the relations among the time series can change over time. Identifying the topologies of such dynamic networks is a major challenge. The second major challenge is that in most practical scenarios, the data is not available at once - it is coming in a streaming fashion. Hence, batch approaches are either not applicable or they become computationally expensive since a batch algorithm is needed to be run when a new datum becomes available. The third challenge is that the multi-dimensional time series data can contain missing values due faulty sensors, privacy and security reasons, or due to saving energy. We address the aforementioned challenges in this dissertation by proposing online/-batch algorithms to solve the problem of time-varying topology identification. A model based on vector autoregressive (VAR) process is adopted initially. The parameters of the VAR model reveal the topology of the underlying network. First, two online algorithms are proposed for the case of streaming data. Next, using the same VAR model, two online algorithms under the framework of online optimization are presented to track the time-varying topologies. To evaluate the performance of propose online algorithms, we show that both the proposed algorithms incur a sublinear static regret. To characterize the performance theoretically in time-varying scenarios, a bound on the dynamic regret for one of the proposed algorithms (TIRSO) is derived. Next, using a structural equation model (SEM) for topology identification, an online algorithm for tracking time-varying topologies is proposed, and a bound on the dynamic regret is also derived for the proposed algorithm. Moreover, using a non-stationary VAR model, an algorithm for dynamic topology identification and breakpoint detection is also proposed, where the notion of local structural breakpoint is introduced to accommodate the concept of breakpoint where instead of the whole topology, only a few edges vary. Finally, the problem of tracking VAR-based time-varying topologies with missing data is investigated. Online algorithms are proposed where the joint signal and topology estimation is carried out. Dynamic regret analysis is also presented for the proposed algorithm. For all the previously mentioned works, simulation tests about the proposed algorithms are also presented and discussed in this dissertation. The numerical results of the proposed algorithms corroborate with the theoretical analysis presented in this dissertation.

• Elnourani, Mohamed & Beferull-Lozano, Baltasar (2020). Non-convex Optimization for Resource Allocation in Wireless Device-to-Device Communications. Universitetet i Agder. ISSN 9788271179953. Full text in Research Archive

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