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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., Comment: 11 pages, 8 figures

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., Comment: 13 pages, 8 figures

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., Comment: 4 figures, 13 pages (original submission 12 pages) Dubmitted to: 4th International Conference on Intelligent Technologies and Applications (INTAP 2021)

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., Comment: 16 pages including supplementary material, published in IEEE Transactions on Signal and Information Processing over Networks

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., Comment: 5 pages, 2 figures, accepted in Globecom 2020

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., Comment: 6 pages, 3 figures, 1 algorithm; Submitted to the European Signal Processing Conference (EUSIPCO) 2020 (Amsterdam)

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., Comment: 6 pages, 2 figures

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., Comment: 23 pages including supplementary material, submitted to IEEE Transactions on Signal Processing

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, as occurs 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 upon this approach and offer a markedly improved estimation performance than existing approaches relying on localization, as demonstrated by simulation studies in indoor scenarios., Comment: 14 pages, 12 figures, 1 table. Submitted to IEEE Transactions on Signal Processing

Learning the dynamics of complex systems features a large number of applications in data science. Graph-based modeling and inference underpins the most prominent family of approaches to learn complex dynamics due to their ability to capture the intrinsic sparsity of direct interactions in such systems. They also provide the user with interpretable graphs that unveil behavioral patterns and changes. To cope with the time-varying nature of interactions, this paper develops an estimation criterion and a solver to learn the parameters of a time-varying vector autoregressive model supported on a network of time series. The notion of local breakpoint is proposed to accommodate changes at individual edges. It contrasts with existing works, which assume that changes at all nodes are aligned in time. Numerical experiments validate the proposed schemes., Comment: 5 pages, 2 figures, conference paper submitted to GlobalSIP2018