arXiv subjects

Antonio G. Marques

Publications and source records attributed to Antonio G. Marques.

At least 37 records · Page 2Linked to original sources

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.

cs.LG↗

arXiv2025

Early Detection of Multidrug Resistance Using Multivariate Time Series Analysis and Interpretable Patient-Similarity Representations

Background and Objectives: Multidrug Resistance (MDR) is a critical global health issue, causing increased hospital stays, healthcare costs, and mortality. This study proposes an interpretable Machine Learning (ML) framework for MDR prediction, aiming for both accurate inference and enhanced explainability. Methods: Patients are modeled as Multivariate Time Series (MTS), capturing clinical progression and patient-to-patient interactions. Similarity among patients is quantified using MTS-based methods: descriptive statistics, Dynamic Time Warping, and Time Cluster Kernel. These similarity measures serve as inputs for MDR classification via Logistic Regression, Random Forest, and Support Vector Machines, with dimensionality reduction and kernel transformations improving model performance. For explainability, patient similarity networks are constructed from these metrics. Spectral clustering and t-SNE are applied to identify MDR-related subgroups and visualize high-risk clusters, enabling insight into clinically relevant patterns. Results: The framework was validated on ICU Electronic Health Records from the University Hospital of Fuenlabrada, achieving an AUC of 81%. It outperforms baseline ML and deep learning models by leveraging graph-based patient similarity. The approach identifies key risk factors -- prolonged antibiotic use, invasive procedures, co-infections, and extended ICU stays -- and reveals clinically meaningful clusters. Code and results are available at \https://github.com/oscarescuderoarnanz/DM4MTS. Conclusions: Patient similarity representations combined with graph-based analysis provide accurate MDR prediction and interpretable insights. This method supports early detection, risk factor identification, and patient stratification, highlighting the potential of explainable ML in critical care.

cs.LG↗

arXiv2025

Matched Topological Subspace Detector

Topological spaces, represented by simplicial complexes, capture richer relationships than graphs by modeling interactions not only between nodes but also among higher-order entities, such as edges or triangles. This motivates the representation of information defined in irregular domains as topological signals. By leveraging the spectral dualities of Hodge and Dirac theory, practical topological signals often concentrate in specific spectral subspaces (e.g., gradient or curl). For instance, in a foreign currency exchange network, the exchange flow signals typically satisfy the arbitrage-free condition and hence are curl-free. However, the presence of anomalies can disrupt these conditions, causing the signals to deviate from such subspaces. In this work, we formulate a hypothesis testing framework to detect whether simplicial complex signals lie in specific subspaces in a principled and tractable manner. Concretely, we propose Neyman-Pearson matched topological subspace detectors for signals defined at a single simplicial level (such as edges) or jointly across all levels of a simplicial complex. The (energy-based projection) proposed detectors handle missing values, provide closed-form performance analysis, and effectively capture the unique topological properties of the data. We demonstrate the effectiveness of the proposed topological detectors on various real-world data, including foreign currency exchange networks.

stat.ML↗

arXiv2025

Deterministic Policy Gradient Primal-Dual Methods for Continuous-Space Constrained MDPs

We study the problem of computing deterministic optimal policies for constrained Markov decision processes (MDPs) with continuous state and action spaces, which are widely encountered in constrained dynamical systems. Designing deterministic policy gradient methods in continuous state and action spaces is particularly challenging due to the lack of enumerable state-action pairs and the adoption of deterministic policies, hindering the application of existing policy gradient methods. To this end, we develop a deterministic policy gradient primal-dual method to find an optimal deterministic policy with non-asymptotic convergence. Specifically, we leverage regularization of the Lagrangian of the constrained MDP to propose a deterministic policy gradient primal-dual (D-PGPD) algorithm that updates the deterministic policy via a quadratic-regularized gradient ascent step and the dual variable via a quadratic-regularized gradient descent step. We prove that the primal-dual iterates of D-PGPD converge at a sub-linear rate to an optimal regularized primal-dual pair. We instantiate D-PGPD with function approximation and prove that the primal-dual iterates of D-PGPD converge at a sub-linear rate to an optimal regularized primal-dual pair, up to a function approximation error. Furthermore, we demonstrate the effectiveness of our method in two continuous control problems: robot navigation and fluid control. This appears to be the first work that proposes a deterministic policy search method for continuous-space constrained MDPs.

cs.AI↗

arXiv2025

Enhancing Graphical Lasso: A Robust Scheme for Non-Stationary Mean Data

This work addresses the problem of graph learning from data following a Gaussian Graphical Model (GGM) with a time-varying mean. Graphical Lasso (GL), the standard method for estimating sparse precision matrices, assumes that the observed data follows a zero-mean Gaussian distribution. However, this assumption is often violated in real-world scenarios where the mean evolves over time due to external influences, trends, or regime shifts. When the mean is not properly accounted for, applying GL directly can lead to estimating a biased precision matrix, hence hindering the graph learning task. To overcome this limitation, we propose Graphical Lasso with Adaptive Targeted Adaptive Importance Sampling (GL-ATAIS), an iterative method that jointly estimates the time-varying mean and the precision matrix. Our approach integrates Bayesian inference with frequentist estimation, leveraging importance sampling to obtain an estimate of the mean while using a regularized maximum likelihood estimator to infer the precision matrix. By iteratively refining both estimates, GL-ATAIS mitigates the bias introduced by time-varying means, leading to more accurate graph recovery. Our numerical evaluation demonstrates the impact of properly accounting for time-dependent means and highlights the advantages of GL-ATAIS over standard GL in recovering the true graph structure.

cs.LG↗

arXiv2025

An MDP Model for Censoring in Harvesting Sensors: Optimal and Approximated Solutions

In this paper, we propose a novel censoring policy for energy-efficient transmissions in energy-harvesting sensors. The problem is formulated as an infinite-horizon Markov Decision Process (MDP). The objective to be optimized is the expected sum of the importance (utility) of all transmitted messages. Assuming that such importance can be evaluated at the transmitting node, we show that, under certain conditions on the battery model, the optimal censoring policy is a threshold function on the importance value. Specifically, messages are transmitted only if their importance is above a threshold whose value depends on the battery level. Exploiting this property, we propose a model-based stochastic scheme that approximates the optimal solution, with less computational complexity and faster convergence speed than a conventional Q-learning algorithm. Numerical experiments in single-hop and multi-hop networks confirm the analytical advantages of the proposed scheme.

eess.SY↗

arXiv2025

A Tensor Low-Rank Approximation for Value Functions in Multi-Task Reinforcement Learning

In pursuit of reinforcement learning systems that could train in physical environments, we investigate multi-task approaches as a means to alleviate the need for massive data acquisition. In a tabular scenario where the Q-functions are collected across tasks, we model our learning problem as optimizing a higher order tensor structure. Recognizing that close-related tasks may require similar actions, our proposed method imposes a low-rank condition on this aggregated Q-tensor. The rationale behind this approach to multi-task learning is that the low-rank structure enforces the notion of similarity, without the need to explicitly prescribe which tasks are similar, but inferring this information from a reduced amount of data simultaneously with the stochastic optimization of the Q-tensor. The efficiency of our low-rank tensor approach to multi-task learning is demonstrated in two numerical experiments, first in a benchmark environment formed by a collection of inverted pendulums, and then into a practical scenario involving multiple wireless communication devices.

cs.LG↗

arXiv2025

Multilinear Tensor Low-Rank Approximation for Policy-Gradient Methods in Reinforcement Learning

Reinforcement learning (RL) aims to estimate the action to take given a (time-varying) state, with the goal of maximizing a cumulative reward function. Predominantly, there are two families of algorithms to solve RL problems: value-based and policy-based methods, with the latter designed to learn a probabilistic parametric policy from states to actions. Most contemporary approaches implement this policy using a neural network (NN). However, NNs usually face issues related to convergence, architectural suitability, hyper-parameter selection, and underutilization of the redundancies of the state-action representations (e.g. locally similar states). This paper postulates multi-linear mappings to efficiently estimate the parameters of the RL policy. More precisely, we leverage the PARAFAC decomposition to design tensor low-rank policies. The key idea involves collecting the policy parameters into a tensor and leveraging tensor-completion techniques to enforce low rank. We establish theoretical guarantees of the proposed methods for various policy classes and validate their efficacy through numerical experiments. Specifically, we demonstrate that tensor low-rank policy models reduce computational and sample complexities in comparison to NN models while achieving similar rewards.

cs.LG↗

arXiv2024

Structure-Guided Input Graph for GNNs facing Heterophily

Graph Neural Networks (GNNs) have emerged as a promising tool to handle data exhibiting an irregular structure. However, most GNN architectures perform well on homophilic datasets, where the labels of neighboring nodes are likely to be the same. In recent years, an increasing body of work has been devoted to the development of GNN architectures for heterophilic datasets, where labels do not exhibit this low-pass behavior. In this work, we create a new graph in which nodes are connected if they share structural characteristics, meaning a higher chance of sharing their labels, and then use this new graph in the GNN architecture. To do this, we compute the k-nearest neighbors graph according to distances between structural features, which are either (i) role-based, such as degree, or (ii) global, such as centrality measures. Experiments show that the labels are smoother in this newly defined graph and that the performance of GNN architectures improves when using this alternative structure.

cs.LG↗

arXiv2024

Exploiting the Structure of Two Graphs with Graph Neural Networks

Graph neural networks (GNNs) have emerged as a promising solution to deal with unstructured data, outperforming traditional deep learning architectures. However, most of the current GNN models are designed to work with a single graph, which limits their applicability in many real-world scenarios where multiple graphs may be involved. To address this limitation, we propose a novel graph-based deep learning architecture to handle tasks where two sets of signals exist, each defined on a different graph. First we consider the setting where the input is represented as a signal on top of one graph (input graph) and the output is a graph signal defined over a different graph (output graph). For this setup, we propose a three-block architecture where we first process the input data using a GNN that operates over the input graph, then apply a transformation function that operates in a latent space and maps the signals from the input to the output graph, and finally implement a second GNN that operates over the output graph. Our goal is not to propose a single specific definition for each of the three blocks, but rather to provide a flexible approach to solve tasks involving data defined on two graphs. The second part of the paper addresses a self-supervised setup, where the focus is not on the output space but on the underlying latent space and, inspired by Canonical Correlation Analysis, we seek informative representations of the data that can be leveraged to solve a downstream task. By leveraging information from multiple graphs, the proposed architecture can capture more intricate relationships between different entities in the data. We test this in several experimental setups using synthetic and real world datasets, and observe that the proposed architecture works better than traditional deep learning architectures, showcasing the importance of leveraging the information of the two graphs.

cs.LG↗

arXiv2024

Low-Rank Tensors for Multi-Dimensional Markov Models

This work presents a low-rank tensor model for multi-dimensional Markov chains. A common approach to simplify the dynamical behavior of a Markov chain is to impose low-rankness on the transition probability matrix. Inspired by the success of these matrix techniques, we present low-rank tensors for representing transition probabilities on multi-dimensional state spaces. Through tensor decomposition, we provide a connection between our method and classical probabilistic models. Moreover, our proposed model yields a parsimonious representation with fewer parameters than matrix-based approaches. Unlike these methods, which impose low-rankness uniformly across all states, our tensor method accounts for the multi-dimensionality of the state space. We also propose an optimization-based approach to estimate a Markov model as a low-rank tensor. Our optimization problem can be solved by the alternating direction method of multipliers (ADMM), which enjoys convergence to a stationary solution. We empirically demonstrate that our tensor model estimates Markov chains more efficiently than conventional techniques, requiring both fewer samples and parameters. We perform numerical simulations for both a synthetic low-rank Markov chain and a real-world example with New York City taxi data, showcasing the advantages of multi-dimensionality for modeling state spaces.

eess.SY↗

arXiv2024

Explainable Spatio-Temporal GCNNs for Irregular Multivariate Time Series: Architecture and Application to ICU Patient Data

In this paper, we present XST-GCNN (eXplainable Spatio-Temporal Graph Convolutional Neural Network), a novel architecture for processing heterogeneous and irregular Multivariate Time Series (MTS) data. Our approach captures temporal and feature dependencies within a unified spatio-temporal pipeline by leveraging a GCNN that uses a spatio-temporal graph aimed at optimizing predictive accuracy and interoperability. For graph estimation, we introduce techniques, including one based on the (heterogeneous) Gower distance. Once estimated, we propose two methods for graph construction: one based on the Cartesian product, treating temporal instants homogeneously, and another spatio-temporal approach with distinct graphs per time step. We also propose two GCNN architectures: a standard GCNN with a normalized adjacency matrix and a higher-order polynomial GCNN. In addition to accuracy, we emphasize explainability by designing an inherently interpretable model and performing a thorough interpretability analysis, identifying key feature-time combinations that drive predictions. We evaluate XST-GCNN using real-world Electronic Health Record data from University Hospital of Fuenlabrada to predict Multidrug Resistance (MDR) in ICU patients, a critical healthcare challenge linked to high mortality and complex treatments. Our architecture outperforms traditional models, achieving a mean ROC-AUC score of 81.03 +- 2.43. Furthermore, the interpretability analysis provides actionable insights into clinical factors driving MDR predictions, enhancing model transparency. This work sets a benchmark for tackling complex inference tasks with heterogeneous MTS, offering a versatile, interpretable solution for real-world applications.

cs.LG↗

arXiv2024

Redesigning graph filter-based GNNs to relax the homophily assumption

Graph neural networks (GNNs) have become a workhorse approach for learning from data defined over irregular domains, typically by implicitly assuming that the data structure is represented by a homophilic graph. However, recent works have revealed that many relevant applications involve heterophilic data where the performance of GNNs can be notably compromised. To address this challenge, we present a simple yet effective architecture designed to mitigate the limitations of the homophily assumption. The proposed architecture reinterprets the role of graph filters in convolutional GNNs, resulting in a more general architecture while incorporating a stronger inductive bias than GNNs based on filter banks. The proposed convolutional layer enhances the expressive capacity of the architecture enabling it to learn from both homophilic and heterophilic data and preventing the issue of oversmoothing. From a theoretical standpoint, we show that the proposed architecture is permutation equivariant. Finally, we show that the proposed GNNs compares favorably relative to several state-of-the-art baselines in both homophilic and heterophilic datasets, showcasing its promising potential.

cs.LG↗

arXiv2024

Online Network Inference from Graph-Stationary Signals with Hidden Nodes

Graph learning is the fundamental task of estimating unknown graph connectivity from available data. Typical approaches assume that not only is all information available simultaneously but also that all nodes can be observed. However, in many real-world scenarios, data can neither be known completely nor obtained all at once. We present a novel method for online graph estimation that accounts for the presence of hidden nodes. We consider signals that are stationary on the underlying graph, which provides a model for the unknown connections to hidden nodes. We then formulate a convex optimization problem for graph learning from streaming, incomplete graph signals. We solve the proposed problem through an efficient proximal gradient algorithm that can run in real-time as data arrives sequentially. Additionally, we provide theoretical conditions under which our online algorithm is similar to batch-wise solutions. Through experimental results on synthetic and real-world data, we demonstrate the viability of our approach for online graph learning in the presence of missing observations.

cs.LG↗

arXiv2024

Tracking Network Dynamics using Probabilistic State-Space Models

This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise estimates, our method accounts for dynamic changes in the network structure over time. We model the network at each timestep as the state of the SSM, and use observations to update beliefs that quantify the probability of the network being in a particular state. Then, by considering the dynamics of transition and observation models through the update and prediction steps, respectively, the proposed method can incorporate the information of real-time graph signals into the beliefs. These beliefs provide a probability distribution of the network at each timestep, being able to provide both an estimate for the network and the uncertainty it entails. Our approach is evaluated through experiments with synthetic and real-world networks. The results demonstrate that our method effectively estimates network states and accounts for the uncertainty in the data, outperforming traditional techniques such as recursive least squares.

eess.SP↗

arXiv2024

A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints

Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based algorithms that can solve bilevel optimization problems with provable guarantees. However, the existing literature mainly focuses on bilevel problems either without constraints, or featuring only simple constraints that do not couple variables across the upper and lower levels, excluding a range of complex applications. Our paper studies this challenging but less explored scenario and develops a (fully) first-order algorithm, which we term BLOCC, to tackle BiLevel Optimization problems with Coupled Constraints. We establish rigorous convergence theory for the proposed algorithm and demonstrate its effectiveness on two well-known real-world applications - hyperparameter selection in support vector machine (SVM) and infrastructure planning in transportation networks using the real data from the city of Seville.

math.OC↗

arXiv2024

Explainable Artificial Intelligence Techniques for Irregular Temporal Classification of Multidrug Resistance Acquisition in Intensive Care Unit Patients

Antimicrobial Resistance represents a significant challenge in the Intensive Care Unit (ICU), where patients are at heightened risk of Multidrug-Resistant (MDR) infections-pathogens resistant to multiple antimicrobial agents. This study introduces a novel methodology that integrates Gated Recurrent Units (GRUs) with advanced intrinsic and post-hoc interpretability techniques for detecting the onset of MDR in patients across time. Within interpretability methods, we propose Explainable Artificial Intelligence (XAI) approaches to handle irregular Multivariate Time Series (MTS), introducing Irregular Time Shapley Additive Explanations (IT-SHAP), a modification of Shapley Additive Explanations designed for irregular MTS with Recurrent Neural Networks focused on temporal outputs. Our methodology aims to identify specific risk factors associated with MDR in ICU patients. GRU with Hadamard's attention demonstrated high initial specificity and increasing sensitivity over time, correlating with increased nosocomial infection risks during prolonged ICU stays. XAI analysis, enhanced by Hadamard attention and IT-SHAP, identified critical factors such as previous non-resistant cultures, specific antibiotic usage patterns, and hospital environment dynamics. These insights suggest that early detection of at-risk patients can inform interventions such as preventive isolation and customized treatments, significantly improving clinical outcomes. The proposed GRU model for temporal classification achieved an average Receiver Operating Characteristic Area Under the Curve of 78.27 +- 1.26 over time, indicating strong predictive performance. In summary, this study highlights the clinical utility of our methodology, which combines predictive accuracy with interpretability, thereby facilitating more effective healthcare interventions by professionals.

cs.LG↗

arXiv2024

Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior

We propose estimating Gaussian graphical models (GGMs) that are fair with respect to sensitive nodal attributes. Many real-world models exhibit unfair discriminatory behavior due to biases in data. Such discrimination is known to be exacerbated when data is equipped with pairwise relationships encoded in a graph. Additionally, the effect of biased data on graphical models is largely underexplored. We thus introduce fairness for graphical models in the form of two bias metrics to promote balance in statistical similarities across nodal groups with different sensitive attributes. Leveraging these metrics, we present Fair GLASSO, a regularized graphical lasso approach to obtain sparse Gaussian precision matrices with unbiased statistical dependencies across groups. We also propose an efficient proximal gradient algorithm to obtain the estimates. Theoretically, we express the tradeoff between fair and accurate estimated precision matrices. Critically, this includes demonstrating when accuracy can be preserved in the presence of a fairness regularizer. On top of this, we study the complexity of Fair GLASSO and demonstrate that our algorithm enjoys a fast convergence rate. Our empirical validation includes synthetic and real-world simulations that illustrate the value and effectiveness of our proposed optimization problem and iterative algorithm.

stat.ML↗