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Antonio G. Marques

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6 papers

1 author row

NeurIPS Conference 2025 Conference Paper

A Few Moments Please: Scalable Graphon Learning via Moment Matching

Reza Ramezanpour
Victor Manuel Tenorio Gomez
Antonio G. Marques
Ashutosh Sabharwal
Santiago Segarra

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.

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AAAI Conference 2025 Conference Paper

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

Sergio Rozada
Dongsheng Ding
Antonio G. Marques
Alejandro Ribeiro

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 for constrained MDPs. 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. To the best of our knowledge, this appears to be the first work that proposes a deterministic policy search method for continuous-space constrained MDPs.

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NeurIPS Conference 2024 Conference Paper

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

Liuyuan Jiang
Quan Xiao
Victor M. Tenorio
Fernando Real-Rojas
Antonio G. Marques
Tianyi Chen

Interest in bilevel optimization has grown in recent years, partially due to its relevance for 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 - support vector machine (SVM) - based model training and infrastructure planning in transportation networks.

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NeurIPS Conference 2024 Conference Paper

Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior

Madeline Navarro
Samuel Rey
Andrei Buciulea
Antonio G. Marques
Santiago Segarra

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.

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JMLR Journal 2022 Journal Article

Joint Inference of Multiple Graphs from Matrix Polynomials

Madeline Navarro
Yuhao Wang
Antonio G. Marques
Caroline Uhler
Santiago Segarra

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, 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. 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 demonstrate the effectiveness of the proposed method with perfect covariance information as well as its robustness in the noisy regime. [abs] [ pdf ][ bib ] &copy JMLR 2022. ( edit, beta )

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JBHI Journal 2021 Journal Article

Data and Network Analytics for COVID-19 ICU Patients: A Case Study for a Spanish Hospital

Sergio Martinez-Aguero
Antonio G. Marques
Inmaculada Mora-Jimenez
Joaquin Alvarez-Rodriguez
Cristina Soguero-Ruiz

The COVID-19 pandemic presents unprecedented challenges to the healthcare systems around the world. In 2020, Spain was among the countries with the highest Intensive Care Unit (ICU) hospitalization and mortality rates. This work analyzes data of COVID-19 patients admitted to a Spanish ICU during the first wave of the pandemic. The patients in our study either died (deceased patients) or were discharged from the ICU (non-deceased patients) and underwent the following landmarks: beginning of symptoms; arrival at the emergency department; beginning of the hospital stay; and ICU admission. Our goal is to create a graph-based data-science methodology to find associations among patients’ comorbidities, previous medication, symptoms, and the COVID-19 treatment, and to analyze their evolution across landmarks. Towards that end, we first perform a hypothesis test based on bootstrap to identify discriminative features among deceased and non-deceased patients. Then, we leverage graph-based representations and network analytics to determine pairwise associations and complex relations among clinical features. The descriptive statistical analysis confirms that deceased patients exhibit multiple comorbidities with stronger levels of association and are treated with a wider range of drugs during the ICU stay. We also observe that the most common treatment was the simultaneous administration of lopinavir/ritonavir with hydroxychloroquine, regardless of the patients’ outcome. Our results illustrate how graph tools and representations yield insights on the relations among comorbidities, drug treatments, and patients’ evolution. All in all, the approach puts forth a new data-analysis tool for clinicians that can be applied to analyze (post-COVID) symptom/patient evolution.

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