arXiv subjects

Antonio G. Marques

Publications and source records attributed to Antonio G. Marques.

At least 19 recordsLinked to original sources

arXiv2026

Sparse Experimental Design for Nonsmooth Estimators via Bilevel Optimization

Optimal experimental design (OED) decides which measurements to acquire for downstream estimation. Classically, this is done by optimizing an information criterion derived from a linear-Gaussian model, for which the estimator is available in closed form. Many modern estimators such as Lasso, elastic net, or total-variation-based estimators, however, are nonsmooth and lack a closed-form solution. To extend OED to these scenarios, we recast the problem as what it implicitly is: a bilevel program whose lower level computes the deployed nonsmooth estimator and whose upper level scores its validation prediction risk. Rather than fixing the number of measurements in advance, we charge each continuous acquisition weight a concave sparsity price. As a result, how many and which measurements to keep are both outcomes of the optimization. A measurement survives only if its estimator-aware value exceeds its price, and progressively increasing the price yields a sequence of designs that explores the trade-off between measurement cardinality and estimation accuracy. Using a value-function penalty reformulation, we develop a single-loop proximal-gradient algorithm that avoids differentiating the nonsmooth solution map and establish its convergence to an (approximate) stationary point. Experiments on synthetic sparse recovery and image reconstruction demonstrate the benefits of the proposed method.

eess.SP↗

arXiv2026

Signal Processing over Product DAGs: Causal Shifts and Filters

We develop a signal processing framework for signals indexed by the product of two directed acyclic graphs (DAGs) and described by a linear structural equation model (SEM). Such a setup arises whenever (linear) causal relations act along two domains, as in component versus manufacturing stage or gene versus experimental condition. Disregarding the factorization of the underlying graph and the native two-axis causal structure requires inverting a weighted transitive closure matrix whose size is the product of the two factor sizes for Fourier analysis. Recognizing that standard graph products fail to yield factorizable transitive closures, we introduce a new DAG product under which separability holds. We motivate the new operator in the vertex domain, and show that it also renders the SEM, the Fourier modes, the causal shifts, and the filters on the product DAG separable across its constituent graph factors.

stat.ML↗

arXiv2026

A Contraction Framework for Stochastic Operators with Bootstrapping: Application to TD Learning

Many iterative algorithms rely on bootstrapping. A variable is updated using a second, frozen copy as a target, which is periodically replaced with the updated variable. Majorize-minimize and inexact proximal-point methods share this structure, as does temporal-difference (TD) learning. However, existing convergence guarantees for scenarios that combine sampled updates with targets refreshed only every $K$ steps rely on the specific structure of the update, such as linear approximation or gradient-based inner steps, and on uniformly bounded sampling error. We instead model the sampled update as a stochastic operator on the parameter space, which reduces the analysis to a contraction argument that needs no gradient structure and allows the sampling error to grow with the iterates. Within this framework, we derive a finite-time bound for i.i.d. samples and any target-update period $K$. We show that the iterates converge geometrically in root mean square to a ball around the fixed point, provided the sensitivity to the frozen target is smaller than the contraction slack of the inner map. Existing deterministic frozen-target contraction and stochastic-gradient-type bounds follow as special cases of our framework, and simulations of TD learning reproduce the predicted contraction rate and scaling of the error floor with the step size.

cs.LG↗

arXiv2026

Learning the Topology of a Simplicial Complex Using Noisy Simplicial Signals

Graphs are a fundamental tool for modeling the irregular (non-Euclidean) structure of complex data. However, they are inherently limited to representing pairwise relationships, making them inadequate for datasets exhibiting higher-order interactions. Simplicial complexes (SCs) have emerged as a promising framework for capturing such higher-order dependencies. This paper focuses on the problem of identifying the topology of an SC from signals, which serves as the foundation for SC-based processing and learning schemes. We consider a setting where we observe noisy signals (features) associated with the nodes of the SC (0-simplices) and a subset of the edges (1-simplices). We assume the observed signals are smooth over the unknown SC topology, and that the higher-order interactions are sparse. Building on these assumptions, we formulate topology learning as a nonconvex optimization problem and propose an efficient block-coordinate descent (BCD) algorithm to solve it. A key step in our formulation is the modeling of the topology of the SC using binary edge and triangle selection vectors, combined with efficient greedy algorithms for optimizing such vectors. We establish theoretical convergence guarantees to a stationary point of a relaxed (penalized) version of the problem and discuss computational complexity. Multiple numerical experiments with both synthetic and real-world datasets validate the effectiveness of our approach, highlighting the capability of SC-learning methods to uncover and model higher-order relationships in complex datasets.

eess.SP↗

arXiv2026

Exact Bayesian Tracking of Dynamic Network Topologies

Tracking the temporal evolution of network topologies is a fundamental challenge in social networks, epidemiology, and sensor systems, among others. This paper develops an exact Bayesian tracker for unweighted, directed graphs using nodal signal observations. This framework yields the full posterior probability distribution over network states at each time step, naturally enabling uncertainty quantification, prediction, and principled decision-making. We model the network dynamics as a Markov process on the Boolean hypercube, where edges transition independently according to a flip probability. For efficient computation, we cast the prediction step as a dyadic convolution, and leverage the Fast Walsh-Hadamard Transform to reduce the computational cost from $\mathcal{O} (4^k)$ to $\mathcal{O} (k 2^k)$, where $k$ is the maximum node degree. When the network transition probabilities are unknown, we develop an Expectation-Maximization framework to learn them from the observed signals. Comprehensive experiments on synthetic and six real-world datasets validate the proposed method and demonstrate its superior tracking accuracy, faster recovery from topological changes, and meaningful uncertainty estimates compared to state-of-the-art and classical baselines.

eess.SP↗

arXiv2026

Directed Graph Topology Inference via Graph Filter Identification

We address the problem of inferring a directed network from nodal measurements generated by linear diffusion dynamics on the sought graph. Observations are modeled as the outputs of a graph convolutional filter, i.e., a polynomial (with unknown coefficients) of a local diffusion graph-shift operator encoding the latent graph topology, excited with an ensemble of independent graph signals with arbitrarily-correlated nodal components. Unlike prior efforts that considered undirected graphs and white signal excitations, here the graph-shift operator and the observations' covariance matrix are not simultaneously diagonalizable. In this challenging context, we first rely on measurements of the output signals along with prior statistical information on the inputs to identify the diffusion filter. Such system identification problem involves solving a system of quadratic matrix equations, which we show is identifiable under spectral-diversity assumptions on the input covariances. For algorithmic purposes we recast it as a smooth quadratic minimization subject to Stiefel manifold constraints. Subsequent identification of the network topology given the graph filter estimate boils down to finding a sparse and structurally admissible shift that commutes with the given filter, thus, forcing the latter to be a polynomial in the sought graph-shift operator. A joint graph filter and topology identification algorithm is also proposed, which alternates between the aforementioned steps in a mutually reinforcing fashion to offer improved sample complexity. Numerical tests corroborate the effectiveness of the proposed algorithms in recovering synthetic digraphs and real-data case studies, and illustrate their potential utility on urban mobility analyses as well as portfolio optimization.

stat.ML↗

arXiv2026

BUILD with Precision: Bottom-Up Inference of Linear DAGs

Learning the structure of directed acyclic graphs (DAGs) from observational data is a central problem in causal discovery, statistical signal processing, and machine learning. Under a linear Gaussian structural equation model (SEM) with equal noise variances, the problem is identifiable and we show that the ensemble precision matrix of the observations exhibits a distinctive structure that facilitates DAG recovery. Exploiting this property, we propose BUILD (Bottom-Up Inference of Linear DAGs), a deterministic stepwise algorithm that identifies leaf nodes and their parents, then prunes the leaves by removing incident edges to proceed to the next step, exactly reconstructing the DAG from the true precision matrix. In practice, precision matrices must be estimated from finite data, and ill-conditioning may lead to error accumulation across BUILD steps. As a mitigation strategy, we periodically re-estimate the precision matrix (with less variables as leaves are pruned), trading off runtime for enhanced robustness. Reproducible results on challenging synthetic benchmarks demonstrate that BUILD compares favorably to state-of-the-art DAG learning algorithms, while offering an explicit handle on complexity.

cs.LG↗

arXiv2026

Addressing Finite-Horizon MDPs via Low-Rank Tensor Value Approximation

We study the problem of learning optimal policies in finite-horizon Markov Decision Processes (MDPs) using low-rank reinforcement learning (RL) methods. In finite-horizon MDPs, the policies, and therefore the value functions (VFs) are not stationary. This aggravates the challenges of high-dimensional MDPs, as they suffer from the curse of dimensionality and high sample complexity. To address these issues, we propose modeling the VFs of finite-horizon MDPs as low-rank tensors, enabling a scalable representation that renders the problem of learning optimal policies tractable. Our approach focuses on VF approximation within a policy iteration framework, where low-rank policy evaluation is combined with greedy policy improvement to compute near-optimal policies. We introduce an optimization-based framework for solving the Bellman equations with low-rank constraints, along with block-coordinate descent (BCD) and block-coordinate gradient descent (BCGD) algorithms, both with theoretical convergence guarantees. We further establish that bounded low-rank policy evaluation error translates into bounded policy improvement in the finite-horizon setting. For scenarios where the system dynamics are unknown, we adapt the proposed BCGD method to estimate the VFs using sampled trajectories. Numerical experiments further demonstrate that the proposed framework reduces computational demands in controlled synthetic scenarios and more realistic resource allocation problems, while achieving competitive policy performance in terms of attained returns.

cs.LG↗

arXiv2026

Learning Product Graphs from Two-dimensional Stationary Signals

Graph learning aims to infer a network structure directly from observed data, enabling the analysis of complex dependencies in irregular domains. Traditional methods focus on scalar signals at each node, ignoring dependencies along additional dimensions such as time, configurations of the observation device, or populations. In this work, we propose a graph signal processing framework for learning graphs from two-dimensional signals, modeled as matrix graph signals generated by joint filtering along both dimensions. This formulation leverages the concept of graph stationarity across the two dimensions and leverages product graph representations to capture structured dependencies. Based on this model, we design an optimization problem that can be solved efficiently and provably recovers the optimal underlying Kronecker/Cartesian/strong product graphs. Experiments on synthetic data demonstrate that our approach achieves higher estimation accuracy and reduced computational cost compared to existing methods.

eess.SP↗

arXiv2026

Precision Neural Networks: Joint Graph And Relational Learning

CoVariance Neural Networks (VNNs) perform convolutions on the graph determined by the covariance matrix of the data, which enables expressive and stable covariance-based learning. However, covariance matrices are typically dense, fail to encode conditional independence, and are often precomputed in a task-agnostic way, which may hinder performance. To overcome these limitations, we study Precision Neural Networks (PNNs), i.e., VNNs on the precision matrix - the inverse covariance. The precision matrix naturally encodes statistical independence, often exhibits sparsity, and preserves the covariance spectral structure. To make precision estimation task-aware, we formulate an optimization problem that jointly learns the network parameters and the precision matrix, and solve it via alternating optimization, by sequentially updating the network weights and the precision estimate. We theoretically bound the distance between the estimated and true precision matrices at each iteration, and demonstrate the effectiveness of joint estimation compared to two-step approaches on synthetic and real-world data.

cs.LG↗

arXiv2025

Joint Network Topology Inference in the Presence of Hidden Nodes

We investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. While most joint inference methods assume that observations are available at all nodes, we consider the realistic and more difficult scenario where a subset of nodes are hidden and cannot be measured. Under the assumptions that the partially observed nodal signals are graph stationary and the networks have similar connectivity patterns, we derive structural characteristics of the connectivity between hidden and observed nodes. This allows us to formulate an optimization problem for estimating networks while accounting for the influence of hidden nodes. We identify conditions under which a convex relaxation yields the sparsest solution, and we formalize the performance of our proposed optimization problem with respect to the effect of the hidden nodes. Finally, synthetic and real-world simulations provide evaluations of our method in comparison with other baselines.

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arXiv2025

Estimating Fair Graphs from Graph-Stationary Data

We estimate fair graphs from graph-stationary nodal observations such that connections are not biased with respect to sensitive attributes. Edges in real-world graphs often exhibit preferences for connecting certain pairs of groups. Biased connections can not only exacerbate but even induce unfair treatment for downstream graph-based tasks. We therefore consider group and individual fairness for graphs corresponding to group- and node-level definitions, respectively. To evaluate the fairness of a given graph, we provide multiple bias metrics, including novel measurements in the spectral domain. Furthermore, we propose Fair Spectral Templates (FairSpecTemp), an optimization-based method with two variants for estimating fair graphs from stationary graph signals, a general model for graph data subsuming many existing ones. One variant of FairSpecTemp exploits commutativity properties of graph stationarity while directly constraining bias, while the other implicitly encourages fair estimates by restricting bias in the graph spectrum and is thus more flexible. Our methods enjoy high probability performance bounds, yielding a conditional tradeoff between fairness and accuracy. In particular, our analysis reveals that accuracy need not be sacrificed to recover fair graphs. We evaluate FairSpecTemp on synthetic and real-world data sets to illustrate its effectiveness and highlight the advantages of both variants of FairSpecTemp.

cs.LG↗

arXiv2025

Graph-Aware Diffusion for Signal Generation

We study the problem of generating graph signals from unknown distributions defined over given graphs, relevant to domains such as recommender systems or sensor networks. Our approach builds on generative diffusion models, which are well established in vision and graph generation but remain underexplored for graph signals. Existing methods lack generality, either ignoring the graph structure in the forward process or designing graph-aware mechanisms tailored to specific domains. We adopt a forward process that incorporates the graph through the heat equation. Rather than relying on the standard formulation, we consider a time-warped coefficient to mitigate the exponential decay of the drift term, yielding a graph-aware generative diffusion model (GAD). We analyze its forward dynamics, proving convergence to a Gaussian Markov random field with covariance parametrized by the graph Laplacian, and interpret the backward dynamics as a sequence of graph-signal denoising problems. Finally, we demonstrate the advantages of GAD on synthetic data, real traffic speed measurements, and a temperature sensor network.

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

Graph signal aware decomposition of dynamic networks via latent graphs

Dynamics on and of networks refer to changes in topology and node-associated signals, respectively and are pervasive in many socio-technological systems, including social, biological, and infrastructure networks. Due to practical constraints, privacy concerns, or malfunctions, we often observe only a fraction of the topological evolution and associated signal, which not only hinders downstream tasks but also restricts our analysis of network evolution. Such aspects could be mitigated by moving our attention at the underlying latent driving factors of the network evolution, which can be naturally uncovered via low-rank tensor decomposition. Tensor-based methods provide a powerful means of uncovering the underlying factors of network evolution through low-rank decompositions. However, the extracted embeddings typically lack a relational structure and are obtained independently from the node signals. This disconnect reduces the interpretability of the embeddings and overlooks the coupling between topology and signals. To address these limitations, we propose a novel two-way decomposition to represent a dynamic graph topology, where the structural evolution is captured by a linear combination of latent graph adjacency matrices reflecting the overall joint evolution of both the topology and the signal. Using spatio-temporal data, we estimate the latent adjacency matrices and their temporal scaling signatures via alternating minimization, and prove that our approach converges to a stationary point. Numerical results show that the proposed method recovers individually and collectively expressive latent graphs, outperforming both standard tensor-based decompositions and signal-based topology identification methods in reconstructing the missing network especially when observations are limited.

eess.SP↗

arXiv2025

Adapting to Heterophilic Graph Data with Structure-Guided Neighbor Discovery

Graph Neural Networks (GNNs) often struggle with heterophilic data, where connected nodes may have dissimilar labels, as they typically assume homophily and rely on local message passing. To address this, we propose creating alternative graph structures by linking nodes with similar structural attributes (e.g., role-based or global), thereby fostering higher label homophily on these new graphs. We theoretically prove that GNN performance can be improved by utilizing graphs with fewer false positive edges (connections between nodes of different classes) and that considering multiple graph views increases the likelihood of finding such beneficial structures. Building on these insights, we introduce Structure-Guided GNN (SG-GNN), an architecture that processes the original graph alongside the newly created structural graphs, adaptively learning to weigh their contributions. Extensive experiments on various benchmark datasets, particularly those with heterophilic characteristics, demonstrate that our SG-GNN achieves state-of-the-art or highly competitive performance, highlighting the efficacy of exploiting structural information to guide GNNs.

cs.LG↗

arXiv2025

A Few Moments Please: Scalable Graphon Learning via Moment Matching

Graphons, as limit objects of dense graph sequences, play a central role in the statistical analysis of network data. However, existing graphon estimation methods often struggle with scalability to large networks and resolution-independent approximation, due to their reliance on estimating latent variables or costly metrics such as the Gromov-Wasserstein distance. In this work, we propose a novel, scalable graphon estimator that directly recovers the graphon via moment matching, leveraging implicit neural representations (INRs). Our approach avoids latent variable modeling by training an INR--mapping coordinates to graphon values--to match empirical subgraph counts (i.e., moments) from observed graphs. This direct estimation mechanism yields a polynomial-time solution and crucially sidesteps the combinatorial complexity of Gromov-Wasserstein optimization. Building on foundational results, we establish a theoretical guarantee: when the observed subgraph motifs sufficiently represent those of the true graphon (a condition met with sufficiently large or numerous graph samples), the estimated graphon achieves a provable upper bound in cut distance from the ground truth. Additionally, we introduce MomentMixup, a data augmentation technique that performs mixup in the moment space to enhance graphon-based learning. Our graphon estimation method achieves strong empirical performance--demonstrating high accuracy on small graphs and superior computational efficiency on large graphs--outperforming state-of-the-art scalable estimators in 75\% of benchmark settings and matching them in the remaining cases. Furthermore, MomentMixup demonstrated improved graph classification accuracy on the majority of our benchmarks.

cs.LG↗

arXiv2025

Graph Guided Diffusion: Unified Guidance for Conditional Graph Generation

Diffusion models have emerged as powerful generative models for graph generation, yet their use for conditional graph generation remains a fundamental challenge. In particular, guiding diffusion models on graphs under arbitrary reward signals is difficult: gradient-based methods, while powerful, are often unsuitable due to the discrete and combinatorial nature of graphs, and non-differentiable rewards further complicate gradient-based guidance. We propose Graph Guided Diffusion (GGDiff), a novel guidance framework that interprets conditional diffusion on graphs as a stochastic control problem to address this challenge. GGDiff unifies multiple guidance strategies, including gradient-based guidance (for differentiable rewards), control-based guidance (using control signals from forward reward evaluations), and zero-order approximations (bridging gradient-based and gradient-free optimization). This comprehensive, plug-and-play framework enables zero-shot guidance of pre-trained diffusion models under both differentiable and non-differentiable reward functions, adapting well-established guidance techniques to graph generation--a direction largely unexplored. Our formulation balances computational efficiency, reward alignment, and sample quality, enabling practical conditional generation across diverse reward types. We demonstrate the efficacy of GGDiff in various tasks, including constraints on graph motifs, fairness, and link prediction, achieving superior alignment with target rewards while maintaining diversity and fidelity.

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