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Gonzalo Mateos

Gonzalo Mateos appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Machine LearningInformation Theorymath.ITSocial and Information Networkseess.SPNetworking and Internet Architecturemath.OCMultiagent SystemsSystems and Controlphysics.soc-phMethodology

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Published work

24 published item(s)

preprint2026arXiv

Exploiting Non-Negativity in DAG Structure Learning

This work addresses the problem of learning directed acyclic graphs (DAGs) from nodal observations generated by a linear structural equation model. DAG learning is a central task in signal processing, machine learning, and causal inference, but it remains challenging because acyclicity is a global combinatorial property. Continuous acyclicity constraints have led to important algorithmic advances by replacing the discrete DAG constraint with smooth equality constraints. However, existing formulations still involve difficult non-convex optimization landscapes and may suffer from degenerate first-order optimality conditions. Here, we restrict attention to DAGs with non-negative edge weights and exploit this additional structure to obtain a simpler characterization of acyclicity. Building on this characterization, we formulate a regularized non-negative DAG learning problem and develop an algorithm based on the method of multipliers. We further analyze the benign optimization landscape induced by non-negativity. In the population regime, we show that the true DAG is the unique global minimizer of the proposed augmented-Lagrangian formulation; moreover, the landscape contains no spurious interior stationary points, and the true DAG is the only acyclic KKT point. Numerical experiments on synthetic and real-world data show that the proposed method improves over state-of-the-art continuous DAG-learning alternatives.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

coVariance Neural Networks

Graph neural networks (GNN) are an effective framework that exploit inter-relationships within graph-structured data for learning. Principal component analysis (PCA) involves the projection of data on the eigenspace of the covariance matrix and draws similarities with the graph convolutional filters in GNNs. Motivated by this observation, we study a GNN architecture, called coVariance neural network (VNN), that operates on sample covariance matrices as graphs. We theoretically establish the stability of VNNs to perturbations in the covariance matrix, thus, implying an advantage over standard PCA-based data analysis approaches that are prone to instability due to principal components associated with close eigenvalues. Our experiments on real-world datasets validate our theoretical results and show that VNN performance is indeed more stable than PCA-based statistical approaches. Moreover, our experiments on multi-resolution datasets also demonstrate that VNNs are amenable to transferability of performance over covariance matrices of different dimensions; a feature that is infeasible for PCA-based approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Learning Graph Structure from Convolutional Mixtures

Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved, noisy, or dynamic, the problem of inferring graph structure from data becomes relevant. In this paper, we postulate a graph convolutional relationship between the observed and latent graphs, and formulate the graph learning task as a network inverse (deconvolution) problem. In lieu of eigendecomposition-based spectral methods or iterative optimization solutions, we unroll and truncate proximal gradient iterations to arrive at a parameterized neural network architecture that we call a Graph Deconvolution Network (GDN). GDNs can learn a distribution of graphs in a supervised fashion, perform link prediction or edge-weight regression tasks by adapting the loss function, and they are inherently inductive. We corroborate GDN's superior graph recovery performance and its generalization to larger graphs using synthetic data in supervised settings. Furthermore, we demonstrate the robustness and representation power of GDNs on real world neuroimaging and social network datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Networks of international football: communities, evolution and globalization of the game

As the most popular sport around the globe, the game of football has recently intrigued much research interest to explore and distill useful and appealing information from the sport. Network science and graph-centric methods have been previously applied to study the importance of football players and teams. In this paper, for the first time we study the macroscopic evolution of the football society from a complex network point of view. Football game records within a time window of over a century were collected and expressed in a graph format, where participant teams are represented by graph nodes and the games between them are the graph edges. We carry out community detection and temporal analysis to reveal the dynamic features and the community structures embedded within the football network, offering the evidence of a continuously expanding football society. Spatio-temporal analysis is also implemented to unveil the temporal states that represent distinct development stages in the football history. Our analysis suggests that the evolution of the game receives considerable impact not only from major sport events, but also from multiple social and political incidents. The game of football and its evolution reflect significant historical transitions and turning points, and can provide a novel perspective for the study of the worldwide globalization process.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Online Change Point Detection for Weighted and Directed Random Dot Product Graphs

Given a sequence of random (directed and weighted) graphs, we address the problem of online monitoring and detection of changes in the underlying data distribution. Our idea is to endow sequential change-point detection (CPD) techniques with a graph representation learning substrate based on the versatile Random Dot Product Graph (RDPG) model. We consider efficient, online updates of a judicious monitoring function, which quantifies the discrepancy between the streaming graph observations and the nominal RDPG. This reference distribution is inferred via spectral embeddings of the first few graphs in the sequence. We characterize the distribution of this running statistic to select thresholds that guarantee error-rate control, and under simplifying approximations we offer insights on the algorithm's detection resolution and delay. The end result is a lightweight online CPD algorithm, that is also explainable by virtue of the well-appreciated interpretability of RDPG embeddings. This is in stark contrast with most existing graph CPD approaches, which either rely on extensive computation, or they store and process the entire observed time series. An apparent limitation of the RDPG model is its suitability for undirected and unweighted graphs only, a gap we aim to close here to broaden the scope of the CPD framework. Unlike previous proposals, our non-parametric RDPG model for weighted graphs does not require a priori specification of the weights' distribution to perform inference and estimation. This network modeling contribution is of independent interest beyond CPD. We offer an open-source implementation of the novel online CPD algorithm for weighted and direct graphs, whose effectiveness and efficiency are demonstrated via (reproducible) synthetic and real network data experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Online Graph Learning under Smoothness Priors

The growing success of graph signal processing (GSP) approaches relies heavily on prior identification of a graph over which network data admit certain regularity. However, adaptation to increasingly dynamic environments as well as demands for real-time processing of streaming data pose major challenges to this end. In this context, we develop novel algorithms for online network topology inference given streaming observations assumed to be smooth on the sought graph. Unlike existing batch algorithms, our goal is to track the (possibly) time-varying network topology while maintaining the memory and computational costs in check by processing graph signals sequentially-in-time. To recover the graph in an online fashion, we leverage proximal gradient (PG) methods to solve a judicious smoothness-regularized, time-varying optimization problem. Under mild technical conditions, we establish that the online graph learning algorithm converges to within a neighborhood of (i.e., it tracks) the optimal time-varying batch solution. Computer simulations using both synthetic and real financial market data illustrate the effectiveness of the proposed algorithm in adapting to streaming signals to track slowly-varying network connectivity.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Graph topology inference benchmarks for machine learning

Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: I) clustering of vertices, II) semi-supervised classification of vertices, III) supervised classification of graph signals, and IV) denoising of graph signals. However, in many practical cases graphs are not explicitly available and must therefore be inferred from data. Validation is a challenging endeavor that naturally depends on the downstream task for which the graph is learnt. Accordingly, it has often been difficult to compare the efficacy of different algorithms. In this work, we introduce several ease-to-use and publicly released benchmarks specifically designed to reveal the relative merits and limitations of graph inference methods. We also contrast some of the most prominent techniques in the literature.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and effect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations' covariance matrix and the so-called graph shift operator (GSO -- a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations' empirical covariance matrix. For streaming data said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Signal Processing on Directed Graphs

This paper provides an overview of the current landscape of signal processing (SP) on directed graphs (digraphs). Directionality is inherent to many real-world (information, transportation, biological) networks and it should play an integral role in processing and learning from network data. We thus lay out a comprehensive review of recent advances in SP on digraphs, offering insights through comparisons with results available for undirected graphs, discussing emerging directions, establishing links with related areas in machine learning and causal inference in statistics, as well as illustrating their practical relevance to timely applications. To this end, we begin by surveying (orthonormal) signal representations and their graph frequency interpretations based on novel measures of signal variation for digraphs. We then move on to filtering, a central component in deriving a comprehensive theory of SP on digraphs. Indeed, through the lens of filter-based generative signal models, we explore a unified framework to study inverse problems (e.g., sampling and deconvolution on networks), statistical analysis of random signals, and topology inference of digraphs from nodal observations.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Network Topology Identification from Spectral Templates

Network topology inference is a cornerstone problem in statistical analyses of complex systems. In this context, the fresh look advocated here permeates benefits from convex optimization and graph signal processing, to identify the so-termed graph shift operator (encoding the network topology) given only the eigenvectors of the shift. These spectral templates can be obtained, for example, from principal component analysis of a set of graph signals defined on the particular network. The novel idea is to find a graph shift that while being consistent with the provided spectral information, it endows the network structure with certain desired properties such as sparsity. The focus is on developing efficient recovery algorithms along with identifiability conditions for two particular shifts, the adjacency matrix and the normalized graph Laplacian. Application domains include network topology identification from steady-state signals generated by a diffusion process, and design of a graph filter that facilitates the distributed implementation of a prescribed linear network operator. Numerical tests showcase the effectiveness of the proposed algorithms in recovering synthetic and structural brain networks.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Network Topology Inference from Spectral Templates

We address the problem of identifying a graph structure from the observation of signals defined on its nodes. Fundamentally, the unknown graph encodes direct relationships between signal elements, which we aim to recover from observable indirect relationships generated by a diffusion process on the graph. The fresh look advocated here permeates benefits from convex optimization and stationarity of graph signals, in order to identify the graph shift operator (a matrix representation of the graph) given only its eigenvectors. These spectral templates can be obtained, e.g., from the sample covariance of independent graph signals diffused on the sought network. The novel idea is to find a graph shift that, while being consistent with the provided spectral information, endows the network with certain desired properties such as sparsity. To that end we develop efficient inference algorithms stemming from provably-tight convex relaxations of natural nonconvex criteria, particularizing the results for two shifts: the adjacency matrix and the normalized Laplacian. Algorithms and theoretical recovery conditions are developed not only when the templates are perfectly known, but also when the eigenvectors are noisy or when only a subset of them are given. Numerical tests showcase the effectiveness of the proposed algorithms in recovering social, brain, and amino-acid networks.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Decentralized learning for wireless communications and networking

This chapter deals with decentralized learning algorithms for in-network processing of graph-valued data. A generic learning problem is formulated and recast into a separable form, which is iteratively minimized using the alternating-direction method of multipliers (ADMM) so as to gain the desired degree of parallelization. Without exchanging elements from the distributed training sets and keeping inter-node communications at affordable levels, the local (per-node) learners consent to the desired quantity inferred globally, meaning the one obtained if the entire training data set were centrally available. Impact of the decentralized learning framework to contemporary wireless communications and networking tasks is illustrated through case studies including target tracking using wireless sensor networks, unveiling Internet traffic anomalies, power system state estimation, as well as spectrum cartography for wireless cognitive radio networks.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Subspace Learning and Imputation for Streaming Big Data Matrices and Tensors

Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well as the need for {\em real-time} processing of streaming data pose major challenges to this end. In this context, the present paper permeates benefits from rank minimization to scalable imputation of missing data, via tracking low-dimensional subspaces and unraveling latent (possibly multi-way) structure from \emph{incomplete streaming} data. For low-rank matrix data, a subspace estimator is proposed based on an exponentially-weighted least-squares criterion regularized with the nuclear norm. After recasting the non-separable nuclear norm into a form amenable to online optimization, real-time algorithms with complementary strengths are developed and their convergence is established under simplifying technical assumptions. In a stationary setting, the asymptotic estimates obtained offer the well-documented performance guarantees of the {\em batch} nuclear-norm regularized estimator. Under the same unifying framework, a novel online (adaptive) algorithm is developed to obtain multi-way decompositions of \emph{low-rank tensors} with missing entries, and perform imputation as a byproduct. Simulated tests with both synthetic as well as real Internet and cardiac magnetic resonance imagery (MRI) data confirm the efficacy of the proposed algorithms, and their superior performance relative to state-of-the-art alternatives.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Dynamic Structural Equation Models for Social Network Topology Inference

Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch an infectious disease, or consumers adopt a trendy electronics product are typically known, and are implicitly dependent on the underlying network. To infer the network topology, a \textit{dynamic} structural equation model is adopted to capture the relationship between observed adoption times and the unknown edge weights. Assuming a slowly time-varying topology and leveraging the sparse connectivity inherent to social networks, edge weights are estimated by minimizing a sparsity-regularized exponentially-weighted least-squares criterion. To this end, solvers with complementary strengths are developed by leveraging (pseudo) real-time sparsity-promoting proximal gradient iterations, the improved convergence rate of accelerated variants, or reduced computational complexity of stochastic gradient descent. Numerical tests with both synthetic and real data demonstrate the effectiveness of the novel algorithms in unveiling sparse dynamically-evolving topologies, while accounting for external influences in the adoption times. Key events in the recent succession of political leadership in North Korea, explain connectivity changes observed in the associated network inferred from global cascades of online media.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Load curve data cleansing and imputation via sparsity and low rank

The smart grid vision is to build an intelligent power network with an unprecedented level of situational awareness and controllability over its services and infrastructure. This paper advocates statistical inference methods to robustify power monitoring tasks against the outlier effects owing to faulty readings and malicious attacks, as well as against missing data due to privacy concerns and communication errors. In this context, a novel load cleansing and imputation scheme is developed leveraging the low intrinsic-dimensionality of spatiotemporal load profiles and the sparse nature of "bad data.'' A robust estimator based on principal components pursuit (PCP) is adopted, which effects a twofold sparsity-promoting regularization through an $\ell_1$-norm of the outliers, and the nuclear norm of the nominal load profiles. Upon recasting the non-separable nuclear norm into a form amenable to decentralized optimization, a distributed (D-) PCP algorithm is developed to carry out the imputation and cleansing tasks using networked devices comprising the so-termed advanced metering infrastructure. If D-PCP converges and a qualification inequality is satisfied, the novel distributed estimator provably attains the performance of its centralized PCP counterpart, which has access to all networkwide data. Computer simulations and tests with real load curve data corroborate the convergence and effectiveness of the novel D-PCP algorithm.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Rank regularization and Bayesian inference for tensor completion and extrapolation

A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities. This probabilistic approach can naturally accommodate general models for the data distribution, lending itself to various fitting criteria that yield optimum estimates in the maximum-a-posteriori sense. In particular, two algorithms are devised for Gaussian- and Poisson-distributed data, that minimize the rank-regularized least-squares error and Kullback-Leibler divergence, respectively. The proposed technique is able to recover the "ground-truth'' tensor rank when tested on synthetic data, and to complete brain imaging and yeast gene expression datasets with 50% and 15% of missing entries respectively, resulting in recovery errors at -10dB and -15dB.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Dynamic Anomalography: Tracking Network Anomalies via Sparsity and Low Rank

In the backbone of large-scale networks, origin-to-destination (OD) traffic flows experience abrupt unusual changes known as traffic volume anomalies, which can result in congestion and limit the extent to which end-user quality of service requirements are met. As a means of maintaining seamless end-user experience in dynamic environments, as well as for ensuring network security, this paper deals with a crucial network monitoring task termed dynamic anomalography. Given link traffic measurements (noisy superpositions of unobserved OD flows) periodically acquired by backbone routers, the goal is to construct an estimated map of anomalies in real time, and thus summarize the network `health state' along both the flow and time dimensions. Leveraging the low intrinsic-dimensionality of OD flows and the sparse nature of anomalies, a novel online estimator is proposed based on an exponentially-weighted least-squares criterion regularized with the sparsity-promoting $\ell_1$-norm of the anomalies, and the nuclear norm of the nominal traffic matrix. After recasting the non-separable nuclear norm into a form amenable to online optimization, a real-time algorithm for dynamic anomalography is developed and its convergence established under simplifying technical assumptions. For operational conditions where computational complexity reductions are at a premium, a lightweight stochastic gradient algorithm based on Nesterov's acceleration technique is developed as well. Comprehensive numerical tests with both synthetic and real network data corroborate the effectiveness of the proposed online algorithms and their tracking capabilities, and demonstrate that they outperform state-of-the-art approaches developed to diagnose traffic anomalies.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Dynamic Network Cartography

Communication networks have evolved from specialized, research and tactical transmission systems to large-scale and highly complex interconnections of intelligent devices, increasingly becoming more commercial, consumer-oriented, and heterogeneous. Propelled by emergent social networking services and high-definition streaming platforms, network traffic has grown explosively thanks to the advances in processing speed and storage capacity of state-of-the-art communication technologies. As "netizens" demand a seamless networking experience that entails not only higher speeds, but also resilience and robustness to failures and malicious cyber-attacks, ample opportunities for signal processing (SP) research arise. The vision is for ubiquitous smart network devices to enable data-driven statistical learning algorithms for distributed, robust, and online network operation and management, adaptable to the dynamically-evolving network landscape with minimal need for human intervention. The present paper aims at delineating the analytical background and the relevance of SP tools to dynamic network monitoring, introducing the SP readership to the concept of dynamic network cartography -- a framework to construct maps of the dynamic network state in an efficient and scalable manner tailored to large-scale heterogeneous networks.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

In-network Sparsity-regularized Rank Minimization: Algorithms and Applications

Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming compressed sensing, matrix completion, and principal components pursuit. This paper develops algorithms for distributed sparsity-regularized rank minimization over networks, when the nuclear- and $\ell_1$-norm are used as surrogates to the rank and nonzero entry counts of the sought matrices, respectively. While nuclear-norm minimization has well-documented merits when centralized processing is viable, non-separability of the singular-value sum challenges its distributed minimization. To overcome this limitation, an alternative characterization of the nuclear norm is adopted which leads to a separable, yet non-convex cost minimized via the alternating-direction method of multipliers. The novel distributed iterations entail reduced-complexity per-node tasks, and affordable message passing among single-hop neighbors. Interestingly, upon convergence the distributed (non-convex) estimator provably attains the global optimum of its centralized counterpart, regardless of initialization. Several application domains are outlined to highlight the generality and impact of the proposed framework. These include unveiling traffic anomalies in backbone networks, predicting networkwide path latencies, and mapping the RF ambiance using wireless cognitive radios. Simulations with synthetic and real network data corroborate the convergence of the novel distributed algorithm, and its centralized performance guarantees.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Recovery of Low-Rank Plus Compressed Sparse Matrices with Application to Unveiling Traffic Anomalies

Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with traffic anomaly detection in backbone networks, and subsumes compressed sensing as well as the timely low-rank plus sparse matrix recovery tasks encountered in matrix decomposition problems. Leveraging the ability of $\ell_1$- and nuclear norms to recover sparse and low-rank matrices, a convex program is formulated to estimate the unknowns. Analysis and simulations confirm that the said convex program can recover the unknowns for sufficiently low-rank and sparse enough components, along with a compression matrix possessing an isometry property when restricted to operate on sparse vectors. When the low-rank, sparse, and compression matrices are drawn from certain random ensembles, it is established that exact recovery is possible with high probability. First-order algorithms are developed to solve the nonsmooth convex optimization problem with provable iteration complexity guarantees. Insightful tests with synthetic and real network data corroborate the effectiveness of the novel approach in unveiling traffic anomalies across flows and time, and its ability to outperform existing alternatives.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Distributed Recursive Least-Squares: Stability and Performance Analysis

The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary processes. In this paper, a distributed recursive least-squares (D-RLS) algorithm is developed for cooperative estimation using ad hoc wireless sensor networks. Distributed iterations are obtained by minimizing a separable reformulation of the exponentially-weighted least-squares cost, using the alternating-minimization algorithm. Sensors carry out reduced-complexity tasks locally, and exchange messages with one-hop neighbors to consent on the network-wide estimates adaptively. A steady-state mean-square error (MSE) performance analysis of D-RLS is conducted, by studying a stochastically-driven `averaged' system that approximates the D-RLS dynamics asymptotically in time. For sensor observations that are linearly related to the time-invariant parameter vector sought, the simplifying independence setting assumptions facilitate deriving accurate closed-form expressions for the MSE steady-state values. The problems of mean- and MSE-sense stability of D-RLS are also investigated, and easily-checkable sufficient conditions are derived under which a steady-state is attained. Without resorting to diminishing step-sizes which compromise the tracking ability of D-RLS, stability ensures that per sensor estimates hover inside a ball of finite radius centered at the true parameter vector, with high-probability, even when inter-sensor communication links are noisy. Interestingly, computer simulations demonstrate that the theoretical findings are accurate also in the pragmatic settings whereby sensors acquire temporally-correlated data.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Robust Nonparametric Regression via Sparsity Control with Application to Load Curve Data Cleansing

Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive sampling, to robustify nonparametric regression against outliers - that is, data markedly deviating from the postulated models. A variational counterpart to least-trimmed squares regression is shown closely related to an L0-(pseudo)norm-regularized estimator, that encourages sparsity in a vector explicitly modeling the outliers. This connection suggests efficient solvers based on convex relaxation, which lead naturally to a variational M-type estimator equivalent to the least-absolute shrinkage and selection operator (Lasso). Outliers are identified by judiciously tuning regularization parameters, which amounts to controlling the sparsity of the outlier vector along the whole robustification path of Lasso solutions. Reduced bias and enhanced generalization capability are attractive features of an improved estimator obtained after replacing the L0-(pseudo)norm with a nonconvex surrogate. The novel robust spline-based smoother is adopted to cleanse load curve data, a key task aiding operational decisions in the envisioned smart grid system. Computer simulations and tests on real load curve data corroborate the effectiveness of the novel sparsity-controlling robust estimators.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In this context, the fresh look advocated here permeates benefits from variable selection and compressive sampling, to robustify PCA against outliers. A least-trimmed squares estimator of a low-rank bilinear factor analysis model is shown closely related to that obtained from an $\ell_0$-(pseudo)norm-regularized criterion encouraging sparsity in a matrix explicitly modeling the outliers. This connection suggests robust PCA schemes based on convex relaxation, which lead naturally to a family of robust estimators encompassing Huber's optimal M-class as a special case. Outliers are identified by tuning a regularization parameter, which amounts to controlling sparsity of the outlier matrix along the whole robustification path of (group) least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its neat ties to robust statistics, the developed outlier-aware PCA framework is versatile to accommodate novel and scalable algorithms to: i) track the low-rank signal subspace robustly, as new data are acquired in real time; and ii) determine principal components robustly in (possibly) infinite-dimensional feature spaces. Synthetic and real data tests corroborate the effectiveness of the proposed robust PCA schemes, when used to identify aberrant responses in personality assessment surveys, as well as unveil communities in social networks, and intruders from video surveillance data.

0 citations0 reviewsNo code linkedOpen access
preprint2010arXiv

Group-Lasso on Splines for Spectrum Cartography

The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and control. Towards this goal, the present paper develops a spline-based approach to field estimation, which relies on a basis expansion model of the field of interest. The model entails known bases, weighted by generic functions estimated from the field's noisy samples. A novel field estimator is developed based on a regularized variational least-squares (LS) criterion that yields finitely-parameterized (function) estimates spanned by thin-plate splines. Robustness considerations motivate well the adoption of an overcomplete set of (possibly overlapping) basis functions, while a sparsifying regularizer augmenting the LS cost endows the estimator with the ability to select a few of these bases that ``better'' explain the data. This parsimonious field representation becomes possible, because the sparsity-aware spline-based method of this paper induces a group-Lasso estimator for the coefficients of the thin-plate spline expansions per basis. A distributed algorithm is also developed to obtain the group-Lasso estimator using a network of wireless sensors, or, using multiple processors to balance the load of a single computational unit. The novel spline-based approach is motivated by a spectrum cartography application, in which a set of sensing cognitive radios collaborate to estimate the distribution of RF power in space and frequency. Simulated tests corroborate that the estimated power spectrum density atlas yields the desired RF state awareness, since the maps reveal spatial locations where idle frequency bands can be reused for transmission, even when fading and shadowing effects are pronounced.

0 citations0 reviewsNo code linkedOpen access