Antoine Souloumiac

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.

Maciej Śliwowski, Matthieu Martin, Antoine Souloumiac et al.

In brain-computer interfaces (BCI) research, recording data is time-consuming and expensive, which limits access to big datasets. This may influence the BCI system performance as machine learning methods depend strongly on the training dataset size. Important questions arise: taking into account neuronal signal characteristics (e.g., non-stationarity), can we achieve higher decoding performance with more data to train decoders? What is the perspective for further improvement with time in the case of long-term BCI studies? In this study, we investigated the impact of long-term recordings on motor imagery decoding from two main perspectives: model requirements regarding dataset size and potential for patient adaptation. We evaluated the multilinear model and two deep learning (DL) models on a long-term BCI and Tetraplegia NCT02550522 clinical trial dataset containing 43 sessions of ECoG recordings performed with a tetraplegic patient. In the experiment, a participant executed 3D virtual hand translation using motor imagery patterns. We designed multiple computational experiments in which training datasets were increased or translated to investigate the relationship between models' performance and different factors influencing recordings. Our analysis showed that adding more data to the training dataset may not instantly increase performance for datasets already containing 40 minutes of the signal. DL decoders showed similar requirements regarding the dataset size compared to the multilinear model while demonstrating higher decoding performance. Moreover, high decoding performance was obtained with relatively small datasets recorded later in the experiment, suggesting motor imagery patterns improvement and patient adaptation. Finally, we proposed UMAP embeddings and local intrinsic dimensionality as a way to visualize the data and potentially evaluate data quality.

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.

Maciej Śliwowski, Matthieu Martin, Antoine Souloumiac et al.

In brain signal processing, deep learning (DL) models have become commonly used. However, the performance gain from using end-to-end DL models compared to conventional ML approaches is usually significant but moderate, typically at the cost of increased computational load and deteriorated explainability. The core idea behind deep learning approaches is scaling the performance with bigger datasets. However, brain signals are temporal data with a low signal-to-noise ratio, uncertain labels, and nonstationary data in time. Those factors may influence the training process and slow down the models' performance improvement. These factors' influence may differ for end-to-end DL model and one using hand-crafted features. As not studied before, this paper compares models that use raw ECoG signal and time-frequency features for BCI motor imagery decoding. We investigate whether the current dataset size is a stronger limitation for any models. Finally, obtained filters were compared to identify differences between hand-crafted features and optimized with backpropagation. To compare the effectiveness of both strategies, we used a multilayer perceptron and a mix of convolutional and LSTM layers that were already proved effective in this task. The analysis was performed on the long-term clinical trial database (almost 600 minutes of recordings) of a tetraplegic patient executing motor imagery tasks for 3D hand translation. For a given dataset, the results showed that end-to-end training might not be significantly better than the hand-crafted features-based model. The performance gap is reduced with bigger datasets, but considering the increased computational load, end-to-end training may not be profitable for this application.

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, Fred Maurice Ngolè Mboula, Antoine Souloumiac

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 $d$.

Maciej Śliwowski, Matthieu Martin, Antoine Souloumiac et al.

Motor brain-computer interfaces (BCIs) are a promising technology that may enable motor-impaired people to interact with their environment. Designing real-time and accurate BCI is crucial to make such devices useful, safe, and easy to use by patients in a real-life environment. Electrocorticography (ECoG)-based BCIs emerge as a good compromise between invasiveness of the recording device and good spatial and temporal resolution of the recorded signal. However, most ECoG signal decoders used to predict continuous hand movements are linear models. These models have a limited representational capacity and may fail to capture the relationship between ECoG signal and continuous hand movements. Deep learning (DL) models, which are state-of-the-art in many problems, could be a solution to better capture this relationship. In this study, we tested several DL-based architectures to predict imagined 3D continuous hand translation using time-frequency features extracted from ECoG signals. The dataset used in the analysis is a part of a long-term clinical trial (ClinicalTrials.gov identifier: NCT02550522) and was acquired during a closed-loop experiment with a tetraplegic subject. The proposed architectures include multilayer perceptron (MLP), convolutional neural networks (CNN), and long short-term memory networks (LSTM). The accuracy of the DL-based and multilinear models was compared offline using cosine similarity. Our results show that CNN-based architectures outperform the current state-of-the-art multilinear model. The best architecture exploited the spatial correlation between neighboring electrodes with CNN and benefited from the sequential character of the desired hand trajectory by using LSTMs. Overall, DL increased the average cosine similarity, compared to the multilinear model, by up to 60%, from 0.189 to 0.302 and from 0.157 to 0.249 for the left and right hand, respectively.

Anne Morvan, Antoine Souloumiac, Krzysztof Choromanski et al.

The aim of this paper is to endow the well-known family of hypercubic quantization hashing methods with theoretical guarantees. In hypercubic quantization, applying a suitable (random or learned) rotation after dimensionality reduction has been experimentally shown to improve the results accuracy in the nearest neighbors search problem. We prove in this paper that the use of these rotations is optimal under some mild assumptions: getting optimal binary sketches is equivalent to applying a rotation uniformizing the diagonal of the covariance matrix between data points. Moreover, for two closed points, the probability to have dissimilar binary sketches is upper bounded by a factor of the initial distance between the data points. Relaxing these assumptions, we obtain a general concentration result for random matrices. We also provide some experiments illustrating these theoretical points and compare a set of algorithms in both the batch and online settings.

Anne Morvan, Antoine Souloumiac, Cédric Gouy-Pailler et al.

In this paper, we address the problem of learning compact similarity-preserving embeddings for massive high-dimensional streams of data in order to perform efficient similarity search. We present a new online method for computing binary compressed representations -sketches- of high-dimensional real feature vectors. Given an expected code length $c$ and high-dimensional input data points, our algorithm provides a $c$-bits binary code for preserving the distance between the points from the original high-dimensional space. Our algorithm does not require neither the storage of the whole dataset nor a chunk, thus it is fully adaptable to the streaming setting. It also provides low time complexity and convergence guarantees. We demonstrate the quality of our binary sketches through experiments on real data for the nearest neighbors search task in the online setting.

Quentin Barthélemy, Cédric Gouy-Pailler, Yoann Isaac et al.

This article addresses the issue of representing electroencephalographic (EEG) signals in an efficient way. While classical approaches use a fixed Gabor dictionary to analyze EEG signals, this article proposes a data-driven method to obtain an adapted dictionary. To reach an efficient dictionary learning, appropriate spatial and temporal modeling is required. Inter-channels links are taken into account in the spatial multivariate model, and shift-invariance is used for the temporal model. Multivariate learned kernels are informative (a few atoms code plentiful energy) and interpretable (the atoms can have a physiological meaning). Using real EEG data, the proposed method is shown to outperform the classical multichannel matching pursuit used with a Gabor dictionary, as measured by the representative power of the learned dictionary and its spatial flexibility. Moreover, dictionary learning can capture interpretable patterns: this ability is illustrated on real data, learning a P300 evoked potential.