Maxime Berar

Paul Peseux, Maxime Berar, Thierry Paquet et al.

Categorical data are present in key areas such as health or supply chain, and this data require specific treatment. In order to apply recent machine learning models on such data, encoding is needed. In order to build interpretable models, one-hot encoding is still a very good solution, but such encoding creates sparse data. Gradient estimators are not suited for sparse data: the gradient is mainly considered as zero while it simply does not always exists, thus a novel gradient estimator is introduced. We show what this estimator minimizes in theory and show its efficiency on different datasets with multiple model architectures. This new estimator performs better than common estimators under similar settings. A real world retail dataset is also released after anonymization. Overall, the aim of this paper is to thoroughly consider categorical data and adapt models and optimizers to these key features.

Alain Rakotomamonjy, Rémi Flamary, Gilles Gasso et al.

We address the problem of unsupervised domain adaptation under the setting of generalized target shift (joint class-conditional and label shifts). For this framework, we theoretically show that, for good generalization, it is necessary to learn a latent representation in which both marginals and class-conditional distributions are aligned across domains. For this sake, we propose a learning problem that minimizes importance weighted loss in the source domain and a Wasserstein distance between weighted marginals. For a proper weighting, we provide an estimator of target label proportion by blending mixture estimation and optimal matching by optimal transport. This estimation comes with theoretical guarantees of correctness under mild assumptions. Our experimental results show that our method performs better on average than competitors across a range domain adaptation problems including \emph{digits},\emph{VisDA} and \emph{Office}. Code for this paper is available at \url{https://github.com/arakotom/mars_domain_adaptation}.

Mohamad Dhaini, Paul Honeine, Maxime Berar et al.

Contrastive learning has demonstrated great success in representation learning, especially for image classification tasks. However, there is still a shortage in studies targeting regression tasks, and more specifically applications on hyperspectral data. In this paper, we propose a spectral-spatial contrastive learning framework for regression tasks for hyperspectral data, in a model-agnostic design allowing to enhance backbones such as 3D convolutional and transformer-based networks. Moreover, we provide a collection of transformations relevant for augmenting hyperspectral data. Experiments on synthetic and real datasets show that the proposed framework and transformations significantly improve the performance of all studied backbone models.

Mohamad Dhaini, Maxime Berar, Paul Honeine et al.

Contrastive learning has demonstrated great effectiveness in representation learning especially for image classification tasks. However, there is still a shortage in the studies targeting regression tasks, and more specifically applications on hyperspectral data. In this paper, we propose a contrastive learning framework for the regression tasks for hyperspectral data. To this end, we provide a collection of transformations relevant for augmenting hyperspectral data, and investigate contrastive learning for regression. Experiments on synthetic and real hyperspectral datasets show that the proposed framework and transformations significantly improve the performance of regression models, achieving better scores than other state-of-the-art transformations.

Romain Mussard, Fannia Pacheco, Maxime Berar et al.

Universal Domain Adaptation (UniDA) aims to transfer knowledge from a labeled source domain to an unlabeled target domain, even when their classes are not fully shared. Few dedicated UniDA methods exist for Time Series (TS), which remains a challenging case. In general, UniDA approaches align common class samples and detect unknown target samples from emerging classes. Such detection often results from thresholding a discriminability metric. The threshold value is typically either a fine-tuned hyperparameter or a fixed value, which limits the ability of the model to adapt to new data. Furthermore, discriminability metrics exhibit overconfidence for unknown samples, leading to misclassifications. This paper introduces UniJDOT, an optimal-transport-based method that accounts for the unknown target samples in the transport cost. Our method also proposes a joint decision space to improve the discriminability of the detection module. In addition, we use an auto-thresholding algorithm to reduce the dependence on fixed or fine-tuned thresholds. Finally, we rely on a Fourier transform-based layer inspired by the Fourier Neural Operator for better TS representation. Experiments on TS benchmarks demonstrate the discriminability, robustness, and state-of-the-art performance of UniJDOT.

Romain Mussard, Fannia Pacheco, Maxime Berar et al.

Deep learning models have significantly improved the ability to detect novelties in time series (TS) data. This success is attributed to their strong representation capabilities. However, due to the inherent variability in TS data, these models often struggle with generalization and robustness. To address this, a common approach is to perform Unsupervised Domain Adaptation, particularly Universal Domain Adaptation (UniDA), to handle domain shifts and emerging novel classes. While extensively studied in computer vision, UniDA remains underexplored for TS data. This work provides a comprehensive implementation and comparison of state-of-the-art TS backbones in a UniDA framework. We propose a reliable protocol to evaluate their robustness and generalization across different domains. The goal is to provide practitioners with a framework that can be easily extended to incorporate future advancements in UniDA and TS architectures. Our results highlight the critical influence of backbone selection in UniDA performance and enable a robustness analysis across various datasets and architectures.

Mokhtar Z. Alaya, Alain Rakotomamonjy, Maxime Berar et al.

Gaussian smoothed sliced Wasserstein distance has been recently introduced for comparing probability distributions, while preserving privacy on the data. It has been shown that it provides performances similar to its non-smoothed (non-private) counterpart. However, the computationaland statistical properties of such a metric have not yet been well-established. This work investigates the theoretical properties of this distance as well as those of generalized versions denoted as Gaussian-smoothed sliced divergences. We first show that smoothing and slicing preserve the metric property and the weak topology. To study the sample complexity of such divergences, we then introduce $\hat{\hatμ}_{n}$ the double empirical distribution for the smoothed-projected $μ$. The distribution $\hat{\hatμ}_{n}$ is a result of a double sampling process: one from sampling according to the origin distribution $μ$ and the second according to the convolution of the projection of $μ$ on the unit sphere and the Gaussian smoothing. We particularly focus on the Gaussian smoothed sliced Wasserstein distance and prove that it converges with a rate $O(n^{-1/2})$. We also derive other properties, including continuity, of different divergences with respect to the smoothing parameter. We support our theoretical findings with empirical studies in the context of privacy-preserving domain adaptation.

Alain Rakotomamonjy, Mokhtar Z. Alaya, Maxime Berar et al.

Gaussian smoothed sliced Wasserstein distance has been recently introduced for comparing probability distributions, while preserving privacy on the data. It has been shown, in applications such as domain adaptation, to provide performances similar to its non-private (non-smoothed) counterpart. However, the computational and statistical properties of such a metric is not yet been well-established. In this paper, we analyze the theoretical properties of this distance as well as those of generalized versions denoted as Gaussian smoothed sliced divergences. We show that smoothing and slicing preserve the metric property and the weak topology. We also provide results on the sample complexity of such divergences. Since, the privacy level depends on the amount of Gaussian smoothing, we analyze the impact of this parameter on the divergence. We support our theoretical findings with empirical studies of Gaussian smoothed and sliced version of Wassertein distance, Sinkhorn divergence and maximum mean discrepancy (MMD). In the context of privacy-preserving domain adaptation, we confirm that those Gaussian smoothed sliced Wasserstein and MMD divergences perform very well while ensuring data privacy.

Mokhtar Z. Alaya, Gilles Gasso, Maxime Berar et al.

Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be supported on the $\textit{same}$ metric space. Because of its high computational complexity, several approximate Wasserstein distances have been proposed based on entropy regularization or on slicing, and one-dimensional Wassserstein computation. In this paper, we propose a novel extension of Wasserstein distance to compare two incomparable distributions, that hinges on the idea of $\textit{distributional slicing}$, embeddings, and on computing the closed-form Wassertein distance between the sliced distributions. We provide a theoretical analysis of this new divergence, called $\textit{heterogeneous Wasserstein discrepancy (HWD)}$, and we show that it preserves several interesting properties including rotation-invariance. We show that the embeddings involved in HWD can be efficiently learned. Finally, we provide a large set of experiments illustrating the behavior of HWD as a divergence in the context of generative modeling and in query framework.

Alain Rakotomamonjy, Abraham Traoré, Maxime Berar et al.

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of distributions to some reference distributions denoted as templates. Our framework extends the theory of similarity of Balcan et al. (2008) to the population distribution case and we show that, for some learning problems, some dissimilarity on distribution achieves low-error linear decision functions with high probability. Our key result is to prove that the theory also holds for empirical distributions. Algorithmically, the proposed approach consists in computing a mapping based on pairwise dissimilarity where learning a linear decision function is amenable. Our experimental results show that the Wasserstein distance embedding performs better than kernel mean embeddings and computing Wasserstein distance is far more tractable than estimating pairwise Kullback-Leibler divergence of empirical distributions.

Florian Yger, Maxime Berar, Gilles Gasso et al.

In this paper, we formulate the Canonical Correlation Analysis (CCA) problem on matrix manifolds. This framework provides a natural way for dealing with matrix constraints and tools for building efficient algorithms even in an adaptive setting. Finally, an adaptive CCA algorithm is proposed and applied to a change detection problem in EEG signals.

Maxime Berar, Françoise Tilotta, Joan Alexis Glaunès et al.

In this paper, we present a computer-assisted method for facial reconstruction. This method provides an estimation of the facial shape associated with unidentified skeletal remains. Current computer-assisted methods using a statistical framework rely on a common set of extracted points located on the bone and soft-tissue surfaces. Most of the facial reconstruction methods then consist of predicting the position of the soft-tissue surface points, when the positions of the bone surface points are known. We propose to use Latent Root Regression for prediction. The results obtained are then compared to those given by Principal Components Analysis linear models. In conjunction, we have evaluated the influence of the number of skull landmarks used. Anatomical skull landmarks are completed iteratively by points located upon geodesics which link these anatomical landmarks, thus enabling us to artificially increase the number of skull points. Facial points are obtained using a mesh-matching algorithm between a common reference mesh and individual soft-tissue surface meshes. The proposed method is validated in term of accuracy, based on a leave-one-out cross-validation test applied to a homogeneous database. Accuracy measures are obtained by computing the distance between the original face surface and its reconstruction. Finally, these results are discussed referring to current computer-assisted reconstruction facial techniques.