arXiv subjects

Antonio G. Marques

Publications and source records attributed to Antonio G. Marques.

At least 73 records · Page 4Linked to original sources

arXiv2022

Enhanced graph-learning schemes driven by similar distributions of motifs

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of motifs of the unknown graph to enhance the inference of classical Gaussian graphical models. Dealing with the density of motifs directly constitutes a challenging combinatorial task. However, we note that if two graphs have similar motif densities, one can show that the expected value of a polynomial applied to their empirical spectral distributions will be similar. Guided by this, we first assume that we have a reference graph that is related to the sought graph (in the sense of having similar motif densities) and then, we exploit this relation by incorporating a similarity constraint and a regularization term in the network topology inference optimization problem. The (non-)convexity of the optimization problem is discussed and a computational efficient alternating majorization-minimization algorithm is designed. We assess the performance of the proposed method through exhaustive numerical experiments where different constraints are considered and compared against popular baselines algorithms on both synthetic and real-world datasets.

eess.SP↗

arXiv2021

Joint inference of multiple graphs with hidden variables from stationary graph signals

Learning graphs from sets of nodal observations represents a prominent problem formally known as graph topology inference. However, current approaches are limited by typically focusing on inferring single networks, and they assume that observations from all nodes are available. First, many contemporary setups involve multiple related networks, and second, it is often the case that only a subset of nodes is observed while the rest remain hidden. Motivated by these facts, we introduce a joint graph topology inference method that models the influence of the hidden variables. Under the assumptions that the observed signals are stationary on the sought graphs and the graphs are closely related, the joint estimation of multiple networks allows us to exploit such relationships to improve the quality of the learned graphs. Moreover, we confront the challenging problem of modeling the influence of the hidden nodes to minimize their detrimental effect. To obtain an amenable approach, we take advantage of the particular structure of the setup at hand and leverage the similarity between the different graphs, which affects both the observed and the hidden nodes. To test the proposed method, numerical simulations over synthetic and real-world graphs are provided.

cs.SI↗

arXiv2021

Learning Graphs from Smooth and Graph-Stationary Signals with Hidden Variables

Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical environments, only a subset of nodes is accessible. A natural (and sometimes effective) approach is to disregard the role of unobserved nodes, but this ignores latent network effects, deteriorating the quality of the estimated graph. Differently, this paper investigates the problem of inferring the topology of a network from nodal observations while taking into account the presence of hidden (latent) variables. Our schemes assume the number of observed nodes is considerably larger than the number of hidden variables and build on recent graph signal processing models to relate the signals and the underlying graph. Specifically, we go beyond classical correlation and partial correlation approaches and assume that the signals are smooth and/or stationary in the sought graph. The assumptions are codified into different constrained optimization problems, with the presence of hidden variables being explicitly taken into account. Since the resulting problems are ill-conditioned and non-convex, the block matrix structure of the proposed formulations is leveraged and suitable convex-regularized relaxations are presented. Numerical experiments over synthetic and real-world datasets showcase the performance of the developed methods and compare them with existing alternatives.

stat.ME↗

arXiv2021

A Robust Alternative for Graph Convolutional Neural Networks via Graph Neighborhood Filters

Graph convolutional neural networks (GCNNs) are popular deep learning architectures that, upon replacing regular convolutions with graph filters (GFs), generalize CNNs to irregular domains. However, classical GFs are prone to numerical errors since they consist of high-order polynomials. This problem is aggravated when several filters are applied in cascade, limiting the practical depth of GCNNs. To tackle this issue, we present the neighborhood graph filters (NGFs), a family of GFs that replaces the powers of the graph shift operator with $k$-hop neighborhood adjacency matrices. NGFs help to alleviate the numerical issues of traditional GFs, allow for the design of deeper GCNNs, and enhance the robustness to errors in the topology of the graph. To illustrate the advantage over traditional GFs in practical applications, we use NGFs in the design of deep neighborhood GCNNs to solve graph signal denoising and node classification problems over both synthetic and real-world data.

eess.SP↗

arXiv2021

Graph-signal Reconstruction and Blind Deconvolution for Structured Inputs

Key to successfully deal with complex contemporary datasets is the development of tractable models that account for the irregular structure of the information at hand. This paper provides a comprehensive and unifying view of several sampling, reconstruction, and recovery problems for signals defined on irregular domains that can be accurately represented by a graph. The workhorse assumption is that the (partially) observed signals can be modeled as the output of a graph filter to a structured (parsimonious) input graph signal. When either the input or the filter coefficients are known, this is tantamount to assuming that the signals of interest live on a subspace defined by the supporting graph. When neither is known, the model becomes bilinear. Upon imposing different priors and additional structure on either the input or the filter coefficients, a broad range of relevant problem formulations arise. The goal is then to leverage those priors, the shift operator of the supporting graph, and the samples of the signal of interest to recover: the signal at the non-sampled nodes (graph-signal interpolation), the input (deconvolution), the filter coefficients (system identification), or any combination thereof (blind deconvolution).

eess.SP↗

arXiv2021

Low-rank State-action Value-function Approximation

Value functions are central to Dynamic Programming and Reinforcement Learning but their exact estimation suffers from the curse of dimensionality, challenging the development of practical value-function (VF) estimation algorithms. Several approaches have been proposed to overcome this issue, from non-parametric schemes that aggregate states or actions to parametric approximations of state and action VFs via, e.g., linear estimators or deep neural networks. Relevantly, several high-dimensional state problems can be well-approximated by an intrinsic low-rank structure. Motivated by this and leveraging results from low-rank optimization, this paper proposes different stochastic algorithms to estimate a low-rank factorization of the $Q(s, a)$ matrix. This is a non-parametric alternative to VF approximation that dramatically reduces the computational and sample complexities relative to classical $Q$-learning methods that estimate $Q(s,a)$ separately for each state-action pair.

cs.AI↗

arXiv2021

Robust graph-filter identification with graph denoising regularization

When approaching graph signal processing tasks, graphs are usually assumed to be perfectly known. However, in many practical applications, the observed (inferred) network is prone to perturbations which, if ignored, will hinder performance. Tailored to those setups, this paper presents a robust formulation for the problem of graph-filter identification from input-output observations. Different from existing works, our approach consists in addressing the robust identification by formulating a joint graph denoising and graph-filter identification problem. Such a problem is formulated as a non-convex optimization, suitable relaxations are proposed, and graph-stationarity assumptions are incorporated to enhance performance. Finally, numerical experiments with synthetic and real-world graphs are used to assess the proposed schemes and compare them with existing (robust) alternatives.

eess.SP↗

arXiv2020

Joint Inference of Multiple Graphs from Matrix Polynomials

Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph and motivated by social and biological networks, we study the problem of jointly inferring multiple graphs from the observation of signals at their nodes (graph signals), which are assumed to be stationary in the sought graphs. From a mathematical point of view, graph stationarity implies that the mapping between the covariance of the signals and the sparse matrix representing the underlying graph is given by a matrix polynomial. A prominent example is that of Markov random fields, where the inverse of the covariance yields the sparse matrix of interest. From a modeling perspective, stationary graph signals can be used to model linear network processes evolving on a set of (not necessarily known) networks. Leveraging that matrix polynomials commute, a convex optimization method along with sufficient conditions that guarantee the recovery of the true graphs are provided when perfect covariance information is available. Particularly important from an empirical viewpoint, we provide high-probability bounds on the recovery error as a function of the number of signals observed and other key problem parameters. Numerical experiments using synthetic and real-world data demonstrate the effectiveness of the proposed method with perfect covariance information as well as its robustness in the noisy regime.

stat.ML↗

arXiv2020

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.

eess.SP↗

arXiv2020

Tensor Graph Convolutional Networks for Multi-relational and Robust Learning

The era of "data deluge" has sparked renewed interest in graph-based learning methods and their widespread applications ranging from sociology and biology to transportation and communications. In this context of graph-aware methods, the present paper introduces a tensor-graph convolutional network (TGCN) for scalable semi-supervised learning (SSL) from data associated with a collection of graphs, that are represented by a tensor. Key aspects of the novel TGCN architecture are the dynamic adaptation to different relations in the tensor graph via learnable weights, and the consideration of graph-based regularizers to promote smoothness and alleviate over-parameterization. The ultimate goal is to design a powerful learning architecture able to: discover complex and highly nonlinear data associations, combine (and select) multiple types of relations, scale gracefully with the graph size, and remain robust to perturbations on the graph edges. The proposed architecture is relevant not only in applications where the nodes are naturally involved in different relations (e.g., a multi-relational graph capturing family, friendship and work relations in a social network), but also in robust learning setups where the graph entails a certain level of uncertainty, and the different tensor slabs correspond to different versions (realizations) of the nominal graph. Numerical tests showcase that the proposed architecture achieves markedly improved performance relative to standard GCNs, copes with state-of-the-art adversarial attacks, and leads to remarkable SSL performance over protein-to-protein interaction networks.

cs.LG↗

arXiv2020

An Underparametrized Deep Decoder Architecture for Graph Signals

While deep convolutional architectures have achieved remarkable results in a gamut of supervised applications dealing with images and speech, recent works show that deep untrained non-convolutional architectures can also outperform state-of-the-art methods in several tasks such as image compression and denoising. Motivated by the fact that many contemporary datasets have an irregular structure different from a 1D/2D grid, this paper generalizes untrained and underparametrized non-convolutional architectures to signals defined over irregular domains represented by graphs. The proposed architecture consists of a succession of layers, each of them implementing an upsampling operator, a linear feature combination, and a scalar nonlinearity. A novel element is the incorporation of upsampling operators accounting for the structure of the supporting graph, which is achieved by considering a systematic graph coarsening approach based on hierarchical clustering. The numerical results carried out in synthetic and real-world datasets showcase that the reconstruction performance can improve drastically if the information of the supporting graph topology is taken into account.

eess.SP↗

arXiv2019

Rethinking Sketching as Sampling: A Graph Signal Processing Approach

Sampling of signals belonging to a low-dimensional subspace has well-documented merits for dimensionality reduction, limited memory storage, and online processing of streaming network data. When the subspace is known, these signals can be modeled as bandlimited graph signals. Most existing sampling methods are designed to minimize the error incurred when reconstructing the original signal from its samples. Oftentimes these parsimonious signals serve as inputs to computationally-intensive linear operators. Hence, interest shifts from reconstructing the signal itself towards approximating the output of the prescribed linear operator efficiently. In this context, we propose a novel sampling scheme that leverages graph signal processing, exploiting the low-dimensional (bandlimited) structure of the input as well as the transformation whose output we wish to approximate. We formulate problems to jointly optimize sample selection and a sketch of the target linear transformation, so when the latter is applied to the sampled input signal the result is close to the desired output. Similar sketching as sampling ideas are also shown effective in the context of linear inverse problems. Because these designs are carried out off line, the resulting sampling plus reduced-complexity processing pipeline is particularly useful for data that are acquired or processed in a sequential fashion, where the linear operator has to be applied fast and repeatedly to successive inputs or response signals. Numerical tests showing the effectiveness of the proposed algorithms include classification of handwritten digits from as few as 20 out of 784 pixels in the input images and selection of sensors from a network deployed to carry out a distributed parameter estimation task.

cs.IT↗

arXiv2019

Generative Adversarial Networks For Graph Data Imputation From Signed Observations

We study the problem of missing data imputation for graph signals from signed one-bit quantized observations. More precisely, we consider that the true graph data is drawn from a distribution of signals that are smooth or bandlimited on a known graph. However, instead of observing these signals, we observe a signed version of them and only at a subset of the nodes on the graph. Our goal is to estimate the true underlying graph signals from our observations. To achieve this, we propose a generative adversarial network (GAN) where the key is to incorporate graph-aware losses in the associated minimax optimization problem. We illustrate the benefits of the proposed method via numerical experiments on hand-written digits from the MNIST dataset

eess.SP↗

arXiv2019

Invariance-Preserving Localized Activation Functions for Graph Neural Networks

Graph signals are signals with an irregular structure that can be described by a graph. Graph neural networks (GNNs) are information processing architectures tailored to these graph signals and made of stacked layers that compose graph convolutional filters with nonlinear activation functions. Graph convolutions endow GNNs with invariance to permutations of the graph nodes' labels. In this paper, we consider the design of trainable nonlinear activation functions that take into consideration the structure of the graph. This is accomplished by using graph median filters and graph max filters, which mimic linear graph convolutions and are shown to retain the permutation invariance of GNNs. We also discuss modifications to the backpropagation algorithm necessary to train local activation functions. The advantages of localized activation function architectures are demonstrated in four numerical experiments: source localization on synthetic graphs, authorship attribution of 19th century novels, movie recommender systems and scientific article classification. In all cases, localized activation functions are shown to improve model capacity.

eess.SP↗

arXiv2019

Estimating Network Processes via Blind Identification of Multiple Graph Filters

This paper studies the problem of jointly estimating multiple network processes driven by a common unknown input, thus effectively generalizing the classical blind multi-channel identification problem to graphs. More precisely, we model network processes as graph filters and consider the observation of multiple graph signals corresponding to outputs of different filters defined on a common graph and driven by the same input. Assuming that the underlying graph is known and the input is unknown, our goal is to recover the specifications of the network processes, namely the coefficients of the graph filters, only relying on the observation of the outputs. Being generated by the same input, these outputs are intimately related and we leverage this relationship for our estimation purposes. Two settings are considered, one where the orders of the filters are known and another one where they are not known. For the former setting, we present a least-squares approach and provide conditions for recovery. For the latter scenario, we propose a sparse recovery algorithm with theoretical performance guarantees. Numerical experiments illustrate the effectiveness of the proposed algorithms, the influence of different parameter settings on the estimation performance, and the validity of our theoretical claims.

eess.SP↗

arXiv2019

Distributed Network Caching via Dynamic Programming

Next-generation communication networks are envisioned to extensively utilize storage-enabled caching units to alleviate unfavorable surges of data traffic by pro-actively storing anticipated highly popular contents across geographically distributed storage devices during off-peak periods. This resource pre-allocation is envisioned not only to improve network efficiency, but also to increase user satisfaction. In this context, the present paper designs optimal caching schemes for \textit{distributed caching} scenarios. In particular, we look at networks where a central node (base station) communicates with a number of "regular" nodes (users or pico base stations) equipped with \textit{local storage} infrastructure. Given the spatio-temporal dynamics of content popularities, and the decentralized nature of our setup, the problem boils down to select what, when and \textit{where} to cache. To address this problem, we define fetching and caching prices that vary across contents, time and space, and formulate a global optimization problem which aggregates the costs across those three domains. The resultant optimization is solved using decomposition and dynamic programming techniques, and a reduced-complexity algorithm is finally proposed. Preliminary simulations illustrating the behavior of our algorithm are finally presented.

cs.NI↗

arXiv2019

A Recurrent Graph Neural Network for Multi-Relational Data

The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for scalable semi-supervised learning from multi-relational data. Key aspects of the novel GRNN architecture are the use of multi-relational graphs, the dynamic adaptation to the different relations via learnable weights, and the consideration of graph-based regularizers to promote smoothness and alleviate over-parametrization. Our ultimate goal is to design a powerful learning architecture able to: discover complex and highly non-linear data associations, combine (and select) multiple types of relations, and scale gracefully with respect to the size of the graph. Numerical tests with real data sets corroborate the design goals and illustrate the performance gains relative to competing alternatives.

cs.LG↗

arXiv2019

Median activation functions for graph neural networks

Graph neural networks (GNNs) have been shown to replicate convolutional neural networks' (CNNs) superior performance in many problems involving graphs. By replacing regular convolutions with linear shift-invariant graph filters (LSI-GFs), GNNs take into account the (irregular) structure of the graph and provide meaningful representations of network data. However, LSI-GFs fail to encode local nonlinear graph signal behavior, and so do regular activation functions, which are nonlinear but pointwise. To address this issue, we propose median activation functions with support on graph neighborhoods instead of individual nodes. A GNN architecture with a trainable multirresolution version of this activation function is then tested on synthetic and real-word datasets, where we show that median activation functions can improve GNN capacity with marginal increase in complexity.

cs.LG↗