arXiv subjects

Eduardo Fernandes Montesuma

Publications and source records attributed to Eduardo Fernandes Montesuma.

At least 19 recordsLinked to original sources

arXiv2026

Gromov-Wasserstein Distillation for Inductive Multi-View Embedding

Gromov-Wasserstein multidimensional scaling (GW-MDS) learns low-dimensional representations from relational data but remains transductive, providing no explicit mapping for unseen samples. We introduce an inductive framework based on barycentric distillation. A GW-MDS teacher learns a latent support and an optimal transport plan from the training data, and barycentric projection converts the resulting coupling into sample-aligned targets. A neural student then learns an explicit out-of-sample mapping, avoiding additional relational-matrix construction and GW optimization at inference. We formulate the approach for single-view data and extend it to Mean-GWMDS and Multi-GWMDS teachers through consensus and selected-projection targets learned by a multi-view student with view-specific encoders. We also investigate a direct neural baseline trained solely with a GW objective. Experiments on synthetic and real-world data using Euclidean, geodesic, and cosine relations show that the distilled models preserve the teacher geometry on unseen samples and consistently outperform direct neural GW training in sample-indexed relational preservation. These results establish barycentric projection as an effective bridge between transductive GW embeddings and inductive neural mappings.

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arXiv2026

Towards Universal Wasserstein Barycenters through Flow Matching

Defining a weighted mean over probability measures under probability metrics is a central tool in probabilistic machine learning. Under the Wasserstein metric, these are called \emph{Wasserstein barycenters}. While most approaches compute barycenters for a fixed weight vector, approximating the whole family of barycenters over the simplex, which we call the \emph{Wasserstein simplex}, remains underexplored. We refer to this problem as \emph{Universal Barycenter Approximation}, and propose \texttt{BaryFM}, a flow matching model transporting the marginal measures into any barycenter in the Wasserstein simplex. Once trained, the network can draw samples from measures in the Wasserstein simplex through an ordinary differential equation. We validate our method on 4 downstream tasks: domain adaptation, generalization, Bayesian posterior aggregation and algorithmic fairness. \texttt{BaryFM} achieves the best average rank among 15 competing methods across 10 domain adaptation benchmarks, matching or surpassing non-universal solvers.

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arXiv2026

Multi-Domain Clustering via Measure Quantization

Clustering is a fundamental task in data analysis, typically addressed through centroid-based methods such as K-means. In this work, we present a general framework for multi-domain clustering via measure quantization: given samples from multiple domains, we learn a shared set of cluster prototypes by minimizing a probability metric, such as the Sinkhorn divergence or the Maximum Mean Discrepancy, between each domain's probability measure and the measure of prototypes. Data points are then assigned to clusters either via nearest centroid, or via optimal transport, a collaborative strategy that couples all samples within a domain. A mini-batch optimization strategy makes both fitting and assignment scalable, reducing memory and computational cost while preserving clustering performance. Experimental results on 5 multi-domain benchmarks spanning image, audio and sensor data show that our Sinkhorn-based method consistently outperforms classical and multi-domain clustering baselines, and that this advantage persists when scaling to hundreds of thousands of samples.

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arXiv2026

Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation

Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not because as they assume access to the complete set of samples from the input measures. Meanwhile, neural network approaches do scale well, but rely on complex optimization problems and cannot easily incorporate label information. We address these limitations through gradient flows in the space of probability measures. Through time discretization, we achieve a scalable algorithm that i) relies on mini-batch optimal transport, ii) accepts modular regularization through task-aware functions, and iii) seamlessly integrates supervised information into the ground-cost. We empirically validate our approach on domain adaptation benchmarks that span computer vision, neuroscience, and chemical engineering. Our method establishes a new state-of-the-art Wasserstein barycenter solver, with labeled barycenters consistently outperforming unlabeled ones. Our code at https://github.com/SigmaNova/barycentric-gradient-flows

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arXiv2026

DeFed-GMM-DaDiL: A Decentralized Federated Framework for Domain Adaptation

Decentralized multi-source domain adaptation seeks to transfer knowledge from multiple heterogeneous and related source domains to an unlabeled target domain in a decentralized setting. We address this challenge through a fully decentralized federated approach, DeFed-GMM-DaDiL, an extension of the GMM-Dataset Dictionary Learning (DaDiL) framework. Each client models its dataset as a Gaussian Mixture Model (GMM), and the federation jointly approximates them via labeled Wasserstein barycenters of shared, learnable GMM atoms. This design enables adaptation without a central server while preserving clients' privacy. We empirically study the stability of the learned representations in scenarios where the target domain has missing classes. Empirical results demonstrate that DeFed-GMM-DaDiL maintains stable and consistent shared representations across clients, effectively reconstructs missing classes, and achieves competitive performance on multi-source domain adaptation benchmarks.

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arXiv2026

Gromov-Wasserstein Methods for Multi-View Relational Embedding and Clustering

Learning low-dimensional representations from multi-view relational data is challenging when underlying geometries differ across views. We propose Bary-GWMDS, a Gromov-Wasserstein-based method that operates directly on distance matrices to learn a consensus embedding preserving shared relational structure. By leveraging intrinsic distances, the approach naturally handles nonlinear distortions across views. We also introduce Mean-GWMDS-C, a clustering-oriented formulation that averages distance matrices and learns reduced-support representations via a consensus Gromov-Wasserstein transport. Experiments on synthetic and real-world datasets show that the proposed framework yields stable and geometrically meaningful embeddings.

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arXiv2026

Structure-Preserving Multi-View Embedding Using Gromov-Wasserstein Optimal Transport

Multi-view data analysis seeks to integrate multiple representations of the same samples in order to recover a coherent low-dimensional structure. Classical approaches often rely on feature concatenation or explicit alignment assumptions, which become restrictive under heterogeneous geometries or nonlinear distortions. In this work, we propose two geometry-aware multi-view embedding strategies grounded in Gromov-Wasserstein (GW) optimal transport. The first, termed Mean-GWMDS, aggregates view-specific relational information by averaging distance matrices and applying GW-based multidimensional scaling to obtain a representative embedding. The second strategy, referred to as Multi-GWMDS, adopts a selection-based paradigm in which multiple geometry-consistent candidate embeddings are generated via GW-based alignment and a representative embedding is selected. Experiments on synthetic manifolds and real-world datasets show that the proposed methods effectively preserve intrinsic relational structure across views. These results highlight GW-based approaches as a flexible and principled framework for multi-view representation learning.

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arXiv2026

ReBaPL: Repulsive Bayesian Prompt Learning

Prompt learning has emerged as an effective technique for fine-tuning large-scale foundation models for downstream tasks. However, conventional prompt learning methods are prone to overfitting and can struggle with out-of-distribution generalization. To address these limitations, Bayesian prompt learning has been proposed, which frames prompt optimization as a Bayesian inference problem to enhance robustness. This paper introduces Repulsive Bayesian Prompt Learning (ReBaPL), a novel method for Bayesian prompt learning, designed to efficiently explore the complex and often multimodal posterior landscape of prompts. Our method integrates a cyclical step-size schedule with a stochastic gradient Hamiltonian Monte Carlo (SGHMC) algorithm, enabling alternating phases of exploration to discover new modes, and exploitation to refine existing modes. Furthermore, we introduce a repulsive force derived from a potential function over probability metrics (including Maximum Mean Discrepancy and Wasserstein distance) computed on the distributions of representations produced by different prompts. This representation-space repulsion diversifies exploration and prevents premature collapse to a single mode. Our approach allows for a more comprehensive characterization of the prompt posterior distribution, leading to improved generalization. In contrast to prior Bayesian prompt learning methods, our method provides a modular plug-and-play Bayesian extension of any existing prompt learning method based on maximum likelihood estimation. We demonstrate the efficacy of ReBaPL on several benchmark datasets, showing superior performance over state-of-the-art prompt learning methods.

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arXiv2025

KD$^{2}$M: A unifying framework for feature knowledge distillation

Knowledge Distillation (KD) seeks to transfer the knowledge of a teacher, towards a student neural net. This process is often done by matching the networks' predictions (i.e., their output), but, recently several works have proposed to match the distributions of neural nets' activations (i.e., their features), a process known as \emph{distribution matching}. In this paper, we propose an unifying framework, Knowledge Distillation through Distribution Matching (KD$^{2}$M), which formalizes this strategy. Our contributions are threefold. We i) provide an overview of distribution metrics used in distribution matching, ii) benchmark on computer vision datasets, and iii) derive new theoretical results for KD.

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arXiv2025

Optimal Transport for Domain Adaptation through Gaussian Mixture Models

Machine learning systems operate under the assumption that training and test data are sampled from a fixed probability distribution. However, this assumptions is rarely verified in practice, as the conditions upon which data was acquired are likely to change. In this context, the adaptation of the unsupervised domain requires minimal access to the data of the new conditions for learning models robust to changes in the data distribution. Optimal transport is a theoretically grounded tool for analyzing changes in distribution, especially as it allows the mapping between domains. However, these methods are usually computationally expensive as their complexity scales cubically with the number of samples. In this work, we explore optimal transport between Gaussian Mixture Models (GMMs), which is conveniently written in terms of the components of source and target GMMs. We experiment with 9 benchmarks, with a total of $85$ adaptation tasks, showing that our methods are more efficient than previous shallow domain adaptation methods, and they scale well with number of samples $n$ and dimensions $d$.

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arXiv2025

Unsupervised Anomaly Detection through Mass Repulsing Optimal Transport

Detecting anomalies in datasets is a longstanding problem in machine learning. In this context, anomalies are defined as a sample that significantly deviates from the remaining data. Meanwhile, optimal transport (OT) is a field of mathematics concerned with the transportation, between two probability measures, at least effort. In classical OT, the optimal transportation strategy of a measure to itself is the identity. In this paper, we tackle anomaly detection by forcing samples to displace its mass, while keeping the least effort objective. We call this new transportation problem Mass Repulsing Optimal Transport (MROT). Naturally, samples lying in low density regions of space will be forced to displace mass very far, incurring a higher transportation cost. We use these concepts to design a new anomaly score. Through a series of experiments in existing benchmarks, and fault detection problems, we show that our algorithm improves over existing methods.

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arXiv2025

A dimensionality reduction technique based on the Gromov-Wasserstein distance

Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new method for dimensionality reduction, based on optimal transportation theory and the Gromov-Wasserstein distance. We offer a new probabilistic view of the classical Multidimensional Scaling (MDS) algorithm and the nonlinear dimensionality reduction algorithm, Isomap (Isometric Mapping or Isometric Feature Mapping) that extends the classical MDS, in which we use the Gromov-Wasserstein distance between the probability measure of high-dimensional data, and its low-dimensional representation. Through gradient descent, our method embeds high-dimensional data into a lower-dimensional space, providing a robust and efficient solution for analyzing complex high-dimensional datasets.

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arXiv2025

Decentralized Federated Dataset Dictionary Learning for Multi-Source Domain Adaptation

Decentralized Multi-Source Domain Adaptation (DMSDA) is a challenging task that aims to transfer knowledge from multiple related and heterogeneous source domains to an unlabeled target domain within a decentralized framework. Our work tackles DMSDA through a fully decentralized federated approach. In particular, we extend the Federated Dataset Dictionary Learning (FedDaDiL) framework by eliminating the necessity for a central server. FedDaDiL leverages Wasserstein barycenters to model the distributional shift across multiple clients, enabling effective adaptation while preserving data privacy. By decentralizing this framework, we enhance its robustness, scalability, and privacy, removing the risk of a single point of failure. We compare our method to its federated counterpart and other benchmark algorithms, showing that our approach effectively adapts source domains to an unlabeled target domain in a fully decentralized manner.

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arXiv2024

Recent Advances in Optimal Transport for Machine Learning

Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to different problems in machine learning, such as generative modeling and transfer learning. In this survey we explore contributions of Optimal Transport for Machine Learning over the period 2012 -- 2023, focusing on four sub-fields of Machine Learning: supervised, unsupervised, transfer and reinforcement learning. We further highlight the recent development in computational Optimal Transport and its extensions, such as partial, unbalanced, Gromov and Neural Optimal Transport, and its interplay with Machine Learning practice.

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arXiv2024

Lighter, Better, Faster Multi-Source Domain Adaptation with Gaussian Mixture Models and Optimal Transport

In this paper, we tackle Multi-Source Domain Adaptation (MSDA), a task in transfer learning where one adapts multiple heterogeneous, labeled source probability measures towards a different, unlabeled target measure. We propose a novel framework for MSDA, based on Optimal Transport (OT) and Gaussian Mixture Models (GMMs). Our framework has two key advantages. First, OT between GMMs can be solved efficiently via linear programming. Second, it provides a convenient model for supervised learning, especially classification, as components in the GMM can be associated with existing classes. Based on the GMM-OT problem, we propose a novel technique for calculating barycenters of GMMs. Based on this novel algorithm, we propose two new strategies for MSDA: GMM-Wasserstein Barycenter Transport (WBT) and GMM-Dataset Dictionary Learning (DaDiL). We empirically evaluate our proposed methods on four benchmarks in image classification and fault diagnosis, showing that we improve over the prior art while being faster and involving fewer parameters. Our code is publicly available at https://github.com/eddardd/gmm_msda

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arXiv2024

Benchmarking Domain Adaptation for Chemical Processes on the Tennessee Eastman Process

In system monitoring, automatic fault diagnosis seeks to infer the systems' state based on sensor readings, e.g., through machine learning models. In this context, it is of key importance that, based on historical data, these systems are able to generalize to incoming data. In parallel, many factors may induce changes in the data probability distribution, hindering the possibility of such models to generalize. In this sense, domain adaptation is an important framework for adapting models to different probability distributions. In this paper, we propose a new benchmark, based on the Tennessee Eastman Process of Downs and Vogel (1993), for benchmarking domain adaptation methods in the context of chemical processes. Besides describing the process, and its relevance for domain adaptation, we describe a series of data processing steps for reproducing our benchmark. We then test 11 domain adaptation strategies on this novel benchmark, showing that optimal transport-based techniques outperform other strategies.

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arXiv2024

Online Multi-Source Domain Adaptation through Gaussian Mixtures and Dataset Dictionary Learning

This paper addresses the challenge of online multi-source domain adaptation (MSDA) in transfer learning, a scenario where one needs to adapt multiple, heterogeneous source domains towards a target domain that comes in a stream. We introduce a novel approach for the online fit of a Gaussian Mixture Model (GMM), based on the Wasserstein geometry of Gaussian measures. We build upon this method and recent developments in dataset dictionary learning for proposing a novel strategy in online MSDA. Experiments on the challenging Tennessee Eastman Process benchmark demonstrate that our approach is able to adapt \emph{on the fly} to the stream of target domain data. Furthermore, our online GMM serves as a memory, representing the whole stream of data.

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arXiv2024

Dataset Dictionary Learning in a Wasserstein Space for Federated Domain Adaptation

Multi-Source Domain Adaptation (MSDA) is a challenging scenario where multiple related and heterogeneous source datasets must be adapted to an unlabeled target dataset. Conventional MSDA methods often overlook that data holders may have privacy concerns, hindering direct data sharing. In response, decentralized MSDA has emerged as a promising strategy to achieve adaptation without centralizing clients' data. Our work proposes a novel approach, Decentralized Dataset Dictionary Learning, to address this challenge. Our method leverages Wasserstein barycenters to model the distributional shift across multiple clients, enabling effective adaptation while preserving data privacy. Specifically, our algorithm expresses each client's underlying distribution as a Wasserstein barycenter of public atoms, weighted by private barycentric coordinates. Our approach ensures that the barycentric coordinates remain undisclosed throughout the adaptation process. Extensive experimentation across five visual domain adaptation benchmarks demonstrates the superiority of our strategy over existing decentralized MSDA techniques. Moreover, our method exhibits enhanced robustness to client parallelism while maintaining relative resilience compared to conventional decentralized MSDA methodologies.

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