arXiv subjects

Gonzalo Mateos

Publications and source records attributed to Gonzalo Mateos.

At least 37 records · Page 2Linked to original sources

arXiv2025

Conformal Inference for Time Series over Graphs

Trustworthy decision making in networked, dynamic environments calls for innovative uncertainty quantification substrates in predictive models for graph time series. Existing conformal prediction (CP) methods have been applied separately to multivariate time series and static graphs, but they either ignore the underlying graph topology or neglect temporal dynamics. To bridge this gap, here we develop a CP-based sequential prediction region framework tailored for graph time series. A key technical innovation is to leverage the graph structure and thus capture pairwise dependencies across nodes, while providing user-specified coverage guarantees on the predictive outcomes. We formally establish that our scheme yields an exponential shrinkage in the volume of the ellipsoidal prediction set relative to its graph-agnostic counterpart. Using real-world datasets, we demonstrate that the novel uncertainty quantification framework maintains desired empirical coverage while achieving markedly smaller (up to 80% reduction) prediction regions than existing approaches.

cs.LG↗

arXiv2025

A Generative Model for Controllable Feature Heterophily in Graphs

We introduce a principled generative framework for graph signals that enables explicit control of feature heterophily, a key property underlying the effectiveness of graph learning methods. Our model combines a Lipschitz graphon-based random graph generator with Gaussian node features filtered through a smooth spectral function of the rescaled Laplacian. We establish new theoretical guarantees: (i) a concentration result for the empirical heterophily score; and (ii) almost-sure convergence of the feature heterophily measure to a deterministic functional of the graphon degree profile, based on a graphon-limit law for polynomial averages of Laplacian eigenvalues. These results elucidate how the interplay between the graphon and the filter governs the limiting level of feature heterophily, providing a tunable mechanism for data modeling and generation. We validate the theory through experiments demonstrating precise control of homophily across graph families and spectral filters.

stat.ML↗

arXiv2025

LASE: Learned Adjacency Spectral Embeddings

We put forth a principled design of a neural architecture to learn nodal Adjacency Spectral Embeddings (ASE) from graph inputs. By bringing to bear the gradient descent (GD) method and leveraging the principle of algorithm unrolling, we truncate and re-interpret each GD iteration as a layer in a graph neural network (GNN) that is trained to approximate the ASE. Accordingly, we call the resulting embeddings and our parametric model Learned ASE (LASE), which is interpretable, parameter efficient, robust to inputs with unobserved edges, and offers controllable complexity during inference. LASE layers combine Graph Convolutional Network (GCN) and fully-connected Graph Attention Network (GAT) modules, which is intuitively pleasing since GCN-based local aggregations alone are insufficient to express the sought graph eigenvectors. We propose several refinements to the unrolled LASE architecture (such as sparse attention in the GAT module and decoupled layerwise parameters) that offer favorable approximation error versus computation tradeoffs; even outperforming heavily-optimized eigendecomposition routines from scientific computing libraries. Because LASE is a differentiable function with respect to its parameters as well as its graph input, we can seamlessly integrate it as a trainable module within a larger (semi-)supervised graph representation learning pipeline. The resulting end-to-end system effectively learns ``discriminative ASEs'' that exhibit competitive performance in supervised link prediction and node classification tasks, outperforming a GNN even when the latter is endowed with open loop, meaning task-agnostic, precomputed spectral positional encodings.

cs.LG↗

arXiv2025

Unrolling Dynamic Programming via Graph Filters

Dynamic programming (DP) is a fundamental tool used across many engineering fields. The main goal of DP is to solve Bellman's optimality equations for a given Markov decision process (MDP). Standard methods like policy iteration exploit the fixed-point nature of these equations to solve them iteratively. However, these algorithms can be computationally expensive when the state-action space is large or when the problem involves long-term dependencies. Here we propose a new approach that unrolls and truncates policy iterations into a learnable parametric model dubbed BellNet, which we train to minimize the so-termed Bellman error from random value function initializations. Viewing the transition probability matrix of the MDP as the adjacency of a weighted directed graph, we draw insights from graph signal processing to interpret (and compactly re-parameterize) BellNet as a cascade of nonlinear graph filters. This fresh look facilitates a concise, transferable, and unifying representation of policy and value iteration, with an explicit handle on complexity during inference. Preliminary experiments conducted in a grid-like environment demonstrate that BellNet can effectively approximate optimal policies in a fraction of the iterations required by classical methods.

cs.AI↗

arXiv2025

Unlearning Algorithmic Biases over Graphs

The growing enforcement of the right to be forgotten regulations has propelled recent advances in certified (graph) unlearning strategies to comply with data removal requests from deployed machine learning (ML) models. Motivated by the well-documented bias amplification predicament inherent to graph data, here we take a fresh look at graph unlearning and leverage it as a bias mitigation tool. Given a pre-trained graph ML model, we develop a training-free unlearning procedure that offers certifiable bias mitigation via a single-step Newton update on the model weights. This way, we contribute a computationally lightweight alternative to the prevalent training- and optimization-based fairness enhancement approaches, with quantifiable performance guarantees. We first develop a novel fairness-aware nodal feature unlearning strategy along with refined certified unlearning bounds for this setting, whose impact extends beyond the realm of graph unlearning. We then design structural unlearning methods endowed with principled selection mechanisms over nodes and edges informed by rigorous bias analyses. Unlearning these judiciously selected elements can mitigate algorithmic biases with minimal impact on downstream utility (e.g., node classification accuracy). Experimental results over real networks corroborate the bias mitigation efficacy of our unlearning strategies, and delineate markedly favorable utility-complexity trade-offs relative to retraining from scratch using augmented graph data obtained via removals.

cs.LG↗

arXiv2025

Explainable Brain Age Gap Prediction in Neurodegenerative Conditions using coVariance Neural Networks

Brain age is the estimate of biological age derived from neuroimaging datasets using machine learning algorithms. Increasing \textit{brain age gap} characterized by an elevated brain age relative to the chronological age can reflect increased vulnerability to neurodegeneration and cognitive decline. Hence, brain age gap is a promising biomarker for monitoring brain health. However, black-box machine learning approaches to brain age gap prediction have limited practical utility. Recent studies on coVariance neural networks (VNN) have proposed a relatively transparent deep learning pipeline for neuroimaging data analyses, which possesses two key features: (i) inherent \textit{anatomically interpretablity} of derived biomarkers; and (ii) a methodologically interpretable perspective based on \textit{linkage with eigenvectors of anatomic covariance matrix}. In this paper, we apply the VNN-based approach to study brain age gap using cortical thickness features for various prevalent neurodegenerative conditions. Our results reveal distinct anatomic patterns for brain age gap in Alzheimer's disease, frontotemporal dementia, and atypical Parkinsonian disorders. Furthermore, we demonstrate that the distinct anatomic patterns of brain age gap are linked with the differences in how VNN leverages the eigenspectrum of the anatomic covariance matrix, thus lending explainability to the reported results.

cs.LG↗

arXiv2024

SLoG-Net: Algorithm Unrolling for Source Localization on Graphs

We present a novel model-based deep learning solution for the inverse problem of localizing sources of network diffusion. Starting from first graph signal processing (GSP) principles, we show that the problem reduces to joint (blind) estimation of the forward diffusion filter and a sparse input signal that encodes the source locations. Despite the bilinear nature of the observations in said blind deconvolution task, by requiring invertibility of the diffusion filter we are able to formulate a convex optimization problem and solve it using the alternating-direction method of multipliers (ADMM). We then unroll and truncate the novel ADMM iterations to arrive at a parameterized neural network architecture for Source Localization on Graphs (SLoG-Net), that we train in an end-to-end fashion using labeled data. This supervised learning approach offers several advantages such as interpretability, parameter efficiency, and controllable complexity during inference. Our reproducible numerical experiments corroborate that SLoG-Net exhibits performance on par with the iterative ADMM baseline, but with markedly faster inference times and without needing to manually tune step-size or penalty parameters. Overall, our approach combines the best of both worlds by incorporating the inductive biases of a GSP model-based solution within a data-driven, trainable deep learning architecture for blind deconvolution of graph signals.

eess.SP↗

arXiv2024

Blind Deconvolution of Graph Signals: Robustness to Graph Perturbations

We study blind deconvolution of signals defined on the nodes of an undirected graph. Although observations are bilinear functions of both unknowns, namely the forward convolutional filter coefficients and the graph signal input, a filter invertibility requirement along with input sparsity allow for an efficient linear programming reformulation. Unlike prior art that relied on perfect knowledge of the graph eigenbasis, here we derive stable recovery conditions in the presence of small graph perturbations. We also contribute a provably convergent robust algorithm, which alternates between blind deconvolution of graph signals and eigenbasis denoising in the Stiefel manifold. Reproducible numerical tests showcase the algorithm's robustness under several graph eigenbasis perturbation models.

eess.SP↗

arXiv2024

Stabilizing the Kumaraswamy Distribution

Large-scale latent variable models require expressive continuous distributions that support efficient sampling and low-variance differentiation, achievable through the reparameterization trick. The Kumaraswamy (KS) distribution is both expressive and supports the reparameterization trick with a simple closed-form inverse CDF. Yet, its adoption remains limited. We identify and resolve numerical instabilities in the inverse CDF and log-pdf, exposing issues in libraries like PyTorch and TensorFlow. We then introduce simple and scalable latent variable models based on the KS, improving exploration-exploitation trade-offs in contextual multi-armed bandits and enhancing uncertainty quantification for link prediction with graph neural networks. Our results support the stabilized KS distribution as a core component in scalable variational models for bounded latent variables.

cs.LG↗

arXiv2024

Online Proximal ADMM for Graph Learning from Streaming Smooth Signals

Graph signal processing deals with algorithms and signal representations that leverage graph structures for multivariate data analysis. Often said graph topology is not readily available and may be time-varying, hence (dynamic) graph structure learning from nodal (e.g., sensor) observations becomes a critical first step. In this paper, we develop a novel algorithm for online graph learning using observation streams, assumed to be smooth on the latent graph. Unlike batch algorithms for topology identification from smooth signals, our modus operandi is to process graph signals sequentially and thus keep memory and computational costs in check. To solve the resulting smoothness-regularized, time-varying inverse problem, we develop online and lightweight iterations built upon the proximal variant of the alternating direction method of multipliers (ADMM), well known for its fast convergence in batch settings. The proximal term in the topology updates seamlessly implements a temporal-variation regularization, and we argue the online procedure exhibits sublinear static regret under some simplifying assumptions. Reproducible experiments with synthetic and real graphs demonstrate the effectiveness of our method in adapting to streaming signals and tracking slowly-varying network connectivity. The proposed approach also exhibits better tracking performance (in terms of suboptimality), when compared to state-of-the-art online graph learning baselines.

eess.SP↗

arXiv2024

Blind Deconvolution on Graphs: Exact and Stable Recovery

We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input signals, a mild requirement on invertibility of the diffusion filter enables an efficient convex relaxation leading to a linear programming formulation that can be tackled with off-the-shelf solvers. Under the Bernoulli-Gaussian model for the inputs, we derive sufficient exact recovery conditions in the noise-free setting. A stable recovery result is then established, ensuring the estimation error remains manageable even when the observations are corrupted by a small amount of noise. Numerical tests with synthetic and real-world network data illustrate the merits of the proposed algorithm, its robustness to noise as well as the benefits of leveraging multiple signals to aid the (blind) localization of sources of diffusion. At a fundamental level, the results presented here broaden the scope of classical blind deconvolution of (spatio-)temporal signals to irregular graph domains.

eess.SP↗

arXiv2024

Non-negative Weighted DAG Structure Learning

We address the problem of learning the topology of directed acyclic graphs (DAGs) from nodal observations, which adhere to a linear structural equation model. Recent advances framed the combinatorial DAG structure learning task as a continuous optimization problem, yet existing methods must contend with the complexities of non-convex optimization. To overcome this limitation, we assume that the latent DAG contains only non-negative edge weights. Leveraging this additional structure, we argue that cycles can be effectively characterized (and prevented) using a convex acyclicity function based on the log-determinant of the adjacency matrix. This convexity allows us to relax the task of learning the non-negative weighted DAG as an abstract convex optimization problem. We propose a DAG recovery algorithm based on the method of multipliers, that is guaranteed to return a global minimizer. Furthermore, we prove that in the infinite sample size regime, the convexity of our approach ensures the recovery of the true DAG structure. We empirically validate the performance of our algorithm in several reproducible synthetic-data test cases, showing that it outperforms state-of-the-art alternatives.

cs.LG↗

arXiv2024

Graph Structure Learning with Interpretable Bayesian Neural Networks

Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse problem with a smoothness promoting objective and rely on iterative methods to obtain a solution. In supervised settings where graph labels are available, one can unroll and truncate these iterations into a deep network that is trained end-to-end. Such a network is parameter efficient and inherits inductive bias from the optimization formulation, an appealing aspect for data constrained settings in, e.g., medicine, finance, and the natural sciences. But typically such settings care equally about uncertainty over edge predictions, not just point estimates. Here we introduce novel iterations with independently interpretable parameters, i.e., parameters whose values - independent of other parameters' settings - proportionally influence characteristics of the estimated graph, such as edge sparsity. After unrolling these iterations, prior knowledge over such graph characteristics shape prior distributions over these independently interpretable network parameters to yield a Bayesian neural network (BNN) capable of graph structure learning (GSL) from smooth signal observations. Fast execution and parameter efficiency allow for high-fidelity posterior approximation via Markov Chain Monte Carlo (MCMC) and thus uncertainty quantification on edge predictions. Synthetic and real data experiments corroborate this model's ability to provide well-calibrated estimates of uncertainty, in test cases that include unveiling economic sector modular structure from S$\&$P$500$ data and recovering pairwise digit similarities from MNIST images. Overall, this framework enables GSL in modest-scale applications where uncertainty on the data structure is paramount.

cs.LG↗

arXiv2024

Convolutional Learning on Directed Acyclic Graphs

We develop a novel convolutional architecture tailored for learning from data defined over directed acyclic graphs (DAGs). DAGs can be used to model causal relationships among variables, but their nilpotent adjacency matrices pose unique challenges towards developing DAG signal processing and machine learning tools. To address this limitation, we harness recent advances offering alternative definitions of causal shifts and convolutions for signals on DAGs. We develop a novel convolutional graph neural network that integrates learnable DAG filters to account for the partial ordering induced by the graph topology, thus providing valuable inductive bias to learn effective representations of DAG-supported data. We discuss the salient advantages and potential limitations of the proposed DAG convolutional network (DCN) and evaluate its performance on two learning tasks using synthetic data: network diffusion estimation and source identification. DCN compares favorably relative to several baselines, showcasing its promising potential.

cs.LG↗

arXiv2024

CoLiDE: Concomitant Linear DAG Estimation

We deal with the combinatorial problem of learning directed acyclic graph (DAG) structure from observational data adhering to a linear structural equation model (SEM). Leveraging advances in differentiable, nonconvex characterizations of acyclicity, recent efforts have advocated a continuous constrained optimization paradigm to efficiently explore the space of DAGs. Most existing methods employ lasso-type score functions to guide this search, which (i) require expensive penalty parameter retuning when the $\textit{unknown}$ SEM noise variances change across problem instances; and (ii) implicitly rely on limiting homoscedasticity assumptions. In this work, we propose a new convex score function for sparsity-aware learning of linear DAGs, which incorporates concomitant estimation of scale and thus effectively decouples the sparsity parameter from the exogenous noise levels. Regularization via a smooth, nonconvex acyclicity penalty term yields CoLiDE ($\textbf{Co}$ncomitant $\textbf{Li}$near $\textbf{D}$AG $\textbf{E}$stimation), a regression-based criterion amenable to efficient gradient computation and closed-form estimation of noise variances in heteroscedastic scenarios. Our algorithm outperforms state-of-the-art methods without incurring added complexity, especially when the DAGs are larger and the noise level profile is heterogeneous. We also find CoLiDE exhibits enhanced stability manifested via reduced standard deviations in several domain-specific metrics, underscoring the robustness of our novel linear DAG estimator.

cs.LG↗

arXiv2024

Towards a Foundation Model for Brain Age Prediction using coVariance Neural Networks

Brain age is the estimate of biological age derived from neuroimaging datasets using machine learning algorithms. Increasing brain age with respect to chronological age can reflect increased vulnerability to neurodegeneration and cognitive decline. In this paper, we study NeuroVNN, based on coVariance neural networks, as a paradigm for foundation model for the brain age prediction application. NeuroVNN is pre-trained as a regression model on healthy population to predict chronological age using cortical thickness features and fine-tuned to estimate brain age in different neurological contexts. Importantly, NeuroVNN adds anatomical interpretability to brain age and has a `scale-free' characteristic that allows its transference to datasets curated according to any arbitrary brain atlas. Our results demonstrate that NeuroVNN can extract biologically plausible brain age estimates in different populations, as well as transfer successfully to datasets of dimensionalities distinct from that for the dataset used to train NeuroVNN.

q-bio.QM↗

arXiv2023

Gradient-Based Spectral Embeddings of Random Dot Product Graphs

The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the dot product of the corresponding latent positions. Accordingly, the embedding task of estimating these vectors from an observed graph is typically posed as a low-rank matrix factorization problem. The workhorse Adjacency Spectral Embedding (ASE) enjoys solid statistical properties, but it is formally solving a surrogate problem and can be computationally intensive. In this paper, we bring to bear recent advances in non-convex optimization and demonstrate their impact to RDPG inference. We advocate first-order gradient descent methods to better solve the embedding problem, and to organically accommodate broader network embedding applications of practical relevance. Notably, we argue that RDPG embeddings of directed graphs loose interpretability unless the factor matrices are constrained to have orthogonal columns. We thus develop a novel feasible optimization method in the resulting manifold. The effectiveness of the graph representation learning framework is demonstrated on reproducible experiments with both synthetic and real network data. Our open-source algorithm implementations are scalable, and unlike the ASE they are robust to missing edge data and can track slowly-varying latent positions from streaming graphs.

cs.LG↗

arXiv2023

Explainable Brain Age Prediction using coVariance Neural Networks

In computational neuroscience, there has been an increased interest in developing machine learning algorithms that leverage brain imaging data to provide estimates of "brain age" for an individual. Importantly, the discordance between brain age and chronological age (referred to as "brain age gap") can capture accelerated aging due to adverse health conditions and therefore, can reflect increased vulnerability towards neurological disease or cognitive impairments. However, widespread adoption of brain age for clinical decision support has been hindered due to lack of transparency and methodological justifications in most existing brain age prediction algorithms. In this paper, we leverage coVariance neural networks (VNN) to propose an explanation-driven and anatomically interpretable framework for brain age prediction using cortical thickness features. Specifically, our brain age prediction framework extends beyond the coarse metric of brain age gap in Alzheimer's disease (AD) and we make two important observations: (i) VNNs can assign anatomical interpretability to elevated brain age gap in AD by identifying contributing brain regions, (ii) the interpretability offered by VNNs is contingent on their ability to exploit specific eigenvectors of the anatomical covariance matrix. Together, these observations facilitate an explainable and anatomically interpretable perspective to the task of brain age prediction.

q-bio.QM↗