Fred Ngolè Mboula

Eduardo Fernandes Montesuma, Fred Ngolè Mboula, Antoine Souloumiac

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.

Eduardo Fernandes Montesuma, Fred Ngolè Mboula, Antoine Souloumiac

This paper seeks to solve Multi-Source Domain Adaptation (MSDA), which aims to mitigate data distribution shifts when transferring knowledge from multiple labeled source domains to an unlabeled target domain. We propose a novel MSDA framework based on dictionary learning and optimal transport. We interpret each domain in MSDA as an empirical distribution. As such, we express each domain as a Wasserstein barycenter of dictionary atoms, which are empirical distributions. We propose a novel algorithm, DaDiL, for learning via mini-batches: (i) atom distributions; (ii) a matrix of barycentric coordinates. Based on our dictionary, we propose two novel methods for MSDA: DaDil-R, based on the reconstruction of labeled samples in the target domain, and DaDiL-E, based on the ensembling of classifiers learned on atom distributions. We evaluate our methods in 3 benchmarks: Caltech-Office, Office 31, and CRWU, where we improved previous state-of-the-art by 3.15%, 2.29%, and 7.71% in classification performance. Finally, we show that interpolations in the Wasserstein hull of learned atoms provide data that can generalize to the target domain.

Eduardo Fernandes Montesuma, Michela Mulas, Fred Ngolè Mboula et al.

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.

Fabiola Espinoza Castellon, Eduardo Fernandes Montesuma, Fred Ngolè Mboula et al.

In this article, we propose an approach for federated domain adaptation, a setting where distributional shift exists among clients and some have unlabeled data. The proposed framework, FedDaDiL, tackles the resulting challenge through dictionary learning of empirical distributions. In our setting, clients' distributions represent particular domains, and FedDaDiL collectively trains a federated dictionary of empirical distributions. In particular, we build upon the Dataset Dictionary Learning framework by designing collaborative communication protocols and aggregation operations. The chosen protocols keep clients' data private, thus enhancing overall privacy compared to its centralized counterpart. We empirically demonstrate that our approach successfully generates labeled data on the target domain with extensive experiments on (i) Caltech-Office, (ii) TEP, and (iii) CWRU benchmarks. Furthermore, we compare our method to its centralized counterpart and other benchmarks in federated domain adaptation.

Eduardo Fernandes Montesuma, Fred Ngolè Mboula, Antoine Souloumiac

In this paper, we consider the intersection of two problems in machine learning: Multi-Source Domain Adaptation (MSDA) and Dataset Distillation (DD). On the one hand, the first considers adapting multiple heterogeneous labeled source domains to an unlabeled target domain. On the other hand, the second attacks the problem of synthesizing a small summary containing all the information about the datasets. We thus consider a new problem called MSDA-DD. To solve it, we adapt previous works in the MSDA literature, such as Wasserstein Barycenter Transport and Dataset Dictionary Learning, as well as DD method Distribution Matching. We thoroughly experiment with this novel problem on four benchmarks (Caltech-Office 10, Tennessee-Eastman Process, Continuous Stirred Tank Reactor, and Case Western Reserve University), where we show that, even with as little as 1 sample per class, one achieves state-of-the-art adaptation performance.

Eduardo Fernandes Montesuma, Fabiola Espinoza Castellon, Fred Ngolè Mboula et al.

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.

Eduardo Fernandes Montesuma, Fred Ngolè Mboula, Antoine Souloumiac

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

Eduardo Fernandes Montesuma, Stevan Le Stanc, Fred Ngolè Mboula

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.

Rebecca Clain, Eduardo Fernandes Montesuma, Fred Ngolè Mboula

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.