Luis M. López-Ramos

Luis M. Lopez-Ramos, Antonio G. Marques, Javier Ramos

Successful deployment of cognitive radios requires efficient sensing of the spectrum and dynamic adaptation of the available resources according to the sensed (imperfect) information. While most works design these two tasks separately, in this paper we address them jointly. In particular, we investigate an overlay cognitive radio with multiple secondary users that access orthogonally a set of frequency bands originally devoted to primary users. The schemes are designed to minimize the cost of sensing, maximize the performance of the secondary users (weighted sum rate), and limit the probability of interfering the primary users. The joint design is addressed using dynamic programming and nonlinear optimization techniques. A two-step strategy that first finds the optimal resource allocation for any sensing scheme and then uses that solution as input to solve for the optimal sensing policy is implemented. The two-step strategy is optimal, gives rise to intuitive optimal policies, and entails a computational complexity much lower than that required to solve the original formulation.

Emilio Ruiz-Moreno, Luis Miguel López-Ramos, Baltasar Beferull-Lozano

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 zero-delay 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 zero-delay 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.

Kevin Roy, Luis Miguel Lopez-Ramos, Baltasar Beferull-Lozano

Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a complexity comparable to linear vector autoregressive (VAR) models while still incorporating nonlinear interactions among different time-series variables. The modeling assumption is that the set of time series is generated in two steps: first, a linear VAR process in a latent space, and second, a set of invertible and Lipschitz continuous nonlinear mappings that are applied per sensor, that is, a component-wise mapping from each latent variable to a variable in the measurement space. The VAR coefficient identification provides a topology representation of the dependencies among the aforementioned variables. The proposed approach models each component-wise nonlinearity using an invertible neural network and imposes sparsity on the VAR coefficients to reflect the parsimonious dependencies usually found in real applications. To efficiently solve the formulated optimization problems, a custom algorithm is devised combining proximal gradient descent, stochastic primal-dual updates, and projection to enforce the corresponding constraints. Experimental results on both synthetic and real data sets show that the proposed algorithm improves the identification of the support of the VAR coefficients in a parsimonious manner while also improving the time-series prediction, as compared to the current state-of-the-art methods.

Emilio Ruiz-Moreno, Luis Miguel López-Ramos, Baltasar Beferull-Lozano

Digitalizing real-world analog signals typically involves sampling in time and discretizing in amplitude. Subsequent signal reconstructions inevitably incur an error that depends on the amplitude resolution and the temporal density of the acquired samples. From an implementation viewpoint, consistent signal reconstruction methods have proven a profitable error-rate decay as the sampling rate increases. Despite that, these results are obtained under offline settings. Therefore, a research gap exists regarding methods for consistent signal reconstruction from data streams. Solving this problem is of great importance because such methods could run at a lower computational cost than the existing offline ones or be used under real-time requirements without losing the benefits of ensuring consistency. In this paper, we formalize for the first time the concept of consistent signal reconstruction from streaming time-series data. Then, we present a signal reconstruction method able to enforce consistency and also exploit the spatiotemporal dependencies of streaming multivariate time-series data to further reduce the signal reconstruction error. Our experiments show that our proposed method achieves a favorable error-rate decay with the sampling rate compared to a similar but non-consistent reconstruction.

Luis M. Lopez-Ramos, Florian Leiser, Aditya Rastogi et al.

The joint implementation of federated learning (FL) and explainable artificial intelligence (XAI) could allow training models from distributed data and explaining their inner workings while preserving essential aspects of privacy. Toward establishing the benefits and tensions associated with their interplay, this scoping review maps the publications that jointly deal with FL and XAI, focusing on publications that reported an interplay between FL and model interpretability or post-hoc explanations. Out of the 37 studies meeting our criteria, only one explicitly and quantitatively analyzed the influence of FL on model explanations, revealing a significant research gap. The aggregation of interpretability metrics across FL nodes created generalized global insights at the expense of node-specific patterns being diluted. Several studies proposed FL algorithms incorporating explanation methods to safeguard the learning process against defaulting or malicious nodes. Studies using established FL libraries or following reporting guidelines are a minority. More quantitative research and structured, transparent practices are needed to fully understand their mutual impact and under which conditions it happens.

Luis Miguel Lopez-Ramos, Kevin Roy, Baltasar Beferull-Lozano

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 modelled 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 back-propagation 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.

Luis M. Lopez-Ramos, Yves Teganya, Baltasar Beferull-Lozano et al.

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 multi-path 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.

Luis Miguel Lopez-Ramos, Baltasar Beferull-Lozano

There is a clear need for efficient algorithms to tune hyperparameters for statistical learning schemes, since the commonly applied search methods (such as grid search with N-fold cross-validation) are inefficient and/or approximate. Previously existing algorithms that efficiently search for hyperparameters relying on the smoothness of the cost function cannot be applied in problems such as Lasso regression. In this contribution, we develop a hyperparameter optimization 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 to yield efficient, data-driven, hyperparameter optimization algorithms. Numerical experiments corroborate the convergence of the proposed method to a local optimum of the LOO validation error curve, and the efficiency of its approximations.

Bakht Zaman, Luis Miguel Lopez Ramos, Daniel Romero et al.

Causality graphs are routinely estimated in social sciences, natural sciences, and engineering due to their capacity to efficiently represent the spatiotemporal structure of multivariate 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.

Luis M. Lopez-Ramos, Vassilis Kekatos, Antonio G. Marques et al.

Smart distribution grids should efficiently integrate stochastic renewable resources while effecting voltage regulation. The design of energy management schemes is challenging, one of the reasons being that energy management is a multistage problem where decisions are not all made at the same timescale and must account for the variability during real-time operation. The joint dispatch of slow- and fast-timescale controls in a smart distribution grid is considered here. The substation voltage, the energy exchanged with a main grid, and the generation schedules for small diesel generators have to be decided on a slow timescale; whereas optimal photovoltaic inverter setpoints are found on a more frequent basis. While inverter and looser voltage regulation limits are imposed at all times, tighter bus voltage constraints are enforced on the average or in probability, thus enabling more efficient renewable integration. Upon reformulating the two-stage grid dispatch as a stochastic convex-concave problem, two distribution-free schemes are put forth. An average dispatch algorithm converges provably to the optimal two-stage decisions via a sequence of convex quadratic programs. Its non-convex probabilistic alternative entails solving two slightly different convex problems and is numerically shown to converge. Numerical tests on a real-world distribution feeder verify that both novel data-driven schemes yield lower costs over competing alternatives.