arXiv subjects

Charles Bouveyron

Publications and source records attributed to Charles Bouveyron.

At least 19 recordsLinked to original sources

arXiv2026

Bridging Maximum Likelihood and Optimal Transport for Efficient Inference and Model Selection in Stochastic Block Models

We study inference in stochastic block models (SBMs) through the lens of optimal transport (OT). We first establish that maximum likelihood variational inference (MLVI) can be interpreted as a semi-relaxed Gromov-Wasserstein (srGW) projection with entropic regularization. While this formulation yields accurate clustering, the entropic regularization prevents transport plans to be sparse, hindering intrinsic model selection. Consequently, we investigate unregularized srGW estimators, and prove that they consistently recover both the SBM connectivity matrix and latent cluster assignments in the asymptotic regime. However, this asymptotic property does not translate into reliable model selection in finite samples, and calls for additional mechanisms to promote sparsity in the inferred cluster proportions. We empirically show that such a regularized formulation yields estimators that simultaneously recover model parameters and select the number of clusters in a single optimization problem, thereby avoiding costly grid search or heuristic model selection procedures.

stat.ML↗

arXiv2025

Parsimonious Gaussian mixture models with piecewise-constant eigenvalue profiles

Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs (with isotropic covariance matrices) certainly lack flexibility to fit certain anisotropic distributions. Connecting these two extremes, we introduce a new family of parsimonious GMMs with piecewise-constant covariance eigenvalue profiles. These extend several low-rank models like the celebrated mixtures of probabilistic principal component analyzers (MPPCA), by enabling any possible sequence of eigenvalue multiplicities. If the latter are prespecified, then we can naturally derive an expectation-maximization (EM) algorithm to learn the mixture parameters. Otherwise, to address the notoriously-challenging issue of jointly learning the mixture parameters and hyperparameters, we propose a componentwise penalized EM algorithm, whose monotonicity is proven. We show the superior likelihood-parsimony tradeoffs achieved by our models on a variety of unsupervised experiments: density fitting, clustering and single-image denoising.

stat.ML↗

arXiv2025

Merging Embedded Topics with Optimal Transport for Online Topic Modeling on Data Streams

Topic modeling is a key component in unsupervised learning, employed to identify topics within a corpus of textual data. The rapid growth of social media generates an ever-growing volume of textual data daily, making online topic modeling methods essential for managing these data streams that continuously arrive over time. This paper introduces a novel approach to online topic modeling named StreamETM. This approach builds on the Embedded Topic Model (ETM) to handle data streams by merging models learned on consecutive partial document batches using unbalanced optimal transport. Additionally, an online change point detection algorithm is employed to identify shifts in topics over time, enabling the identification of significant changes in the dynamics of text streams. Numerical experiments on simulated and real-world data show StreamETM outperforming competitors. We provide the code publicly available at https://github.com/fgranese/StreamETM.

cs.LG↗

arXiv2025

Stick-Breaking Embedded Topic Model with Continuous Optimal Transport for Online Analysis of Document Streams

Online topic models are unsupervised algorithms to identify latent topics in data streams that continuously evolve over time. Although these methods naturally align with real-world scenarios, they have received considerably less attention from the community compared to their offline counterparts, due to specific additional challenges. To tackle these issues, we present SB-SETM, an innovative model extending the Embedded Topic Model (ETM) to process data streams by merging models formed on successive partial document batches. To this end, SB-SETM (i) leverages a truncated stick-breaking construction for the topic-per-document distribution, enabling the model to automatically infer from the data the appropriate number of active topics at each timestep; and (ii) introduces a merging strategy for topic embeddings based on a continuous formulation of optimal transport adapted to the high dimensionality of the latent topic space. Numerical experiments show SB-SETM outperforming baselines on simulated scenarios. We extensively test it on a real-world corpus of news articles covering the Russian-Ukrainian war throughout 2022-2023.

cs.LG↗

arXiv2024

The Deep Latent Position Block Model For The Block Clustering And Latent Representation Of Networks

The increased quantity of data has led to a soaring use of networks to model relationships between different objects, represented as nodes. Since the number of nodes can be particularly large, the network information must be summarised through node clustering methods. In order to make the results interpretable, a relevant visualisation of the network is also required. To tackle both issues, we propose a new methodology called deep latent position block model (Deep LPBM) which simultaneously provides a network visualisation coherent with block modelling, allowing a clustering more general than community detection methods, as well as a continuous representation of nodes in a latent space given by partial membership vectors. Our methodology is based on a variational autoencoder strategy, relying on a graph convolutional network, with a specifically designed decoder. The inference is done using both variational and stochastic approximations. In order to efficiently select the number of clusters, we provide a comparison of three model selection criteria. An extensive benchmark as well as an evaluation of the partial memberships are provided. We conclude with an analysis of a French political blogosphere network and a comparison with another methodology to illustrate the insights provided by Deep LPBM results.

stat.ME↗

arXiv2024

Sparse and geometry-aware generalisation of the mutual information for joint discriminative clustering and feature selection

Feature selection in clustering is a hard task which involves simultaneously the discovery of relevant clusters as well as relevant variables with respect to these clusters. While feature selection algorithms are often model-based through optimised model selection or strong assumptions on the data distribution, we introduce a discriminative clustering model trying to maximise a geometry-aware generalisation of the mutual information called GEMINI with a simple l1 penalty: the Sparse GEMINI. This algorithm avoids the burden of combinatorial feature subset exploration and is easily scalable to high-dimensional data and large amounts of samples while only designing a discriminative clustering model. We demonstrate the performances of Sparse GEMINI on synthetic datasets and large-scale datasets. Our results show that Sparse GEMINI is a competitive algorithm and has the ability to select relevant subsets of variables with respect to the clustering without using relevance criteria or prior hypotheses.

stat.ML↗

arXiv2024

The Deep Latent Position Topic Model for Clustering and Representation of Networks with Textual Edges

Numerical interactions leading to users sharing textual content published by others are naturally represented by a network where the individuals are associated with the nodes and the exchanged texts with the edges. To understand those heterogeneous and complex data structures, clustering nodes into homogeneous groups as well as rendering a comprehensible visualisation of the data is mandatory. To address both issues, we introduce Deep-LPTM, a model-based clustering strategy relying on a variational graph auto-encoder approach as well as a probabilistic model to characterise the topics of discussion. Deep-LPTM allows to build a joint representation of the nodes and of the edges in two embeddings spaces. The parameters are inferred using a variational inference algorithm. We also introduce IC2L, a model selection criterion specifically designed to choose models with relevant clustering and visualisation properties. An extensive benchmark study on synthetic data is provided. In particular, we find that Deep-LPTM better recovers the partitions of the nodes than the state-of-the art ETSBM and STBM. Eventually, the emails of the Enron company are analysed and visualisations of the results are presented, with meaningful highlights of the graph structure.

cs.LG↗

arXiv2023

Generalised Mutual Information: a Framework for Discriminative Clustering

In the last decade, recent successes in deep clustering majorly involved the Mutual Information (MI) as an unsupervised objective for training neural networks with increasing regularisations. While the quality of the regularisations have been largely discussed for improvements, little attention has been dedicated to the relevance of MI as a clustering objective. In this paper, we first highlight how the maximisation of MI does not lead to satisfying clusters. We identified the Kullback-Leibler divergence as the main reason of this behaviour. Hence, we generalise the mutual information by changing its core distance, introducing the Generalised Mutual Information (GEMINI): a set of metrics for unsupervised neural network training. Unlike MI, some GEMINIs do not require regularisations when training as they are geometry-aware thanks to distances or kernels in the data space. Finally, we highlight that GEMINIs can automatically select a relevant number of clusters, a property that has been little studied in deep discriminative clustering context where the number of clusters is a priori unknown.

stat.ML↗

arXiv2023

Embedded Topics in the Stochastic Block Model

Communication networks such as emails or social networks are now ubiquitous and their analysis has become a strategic field. In many applications, the goal is to automatically extract relevant information by looking at the nodes and their connections. Unfortunately, most of the existing methods focus on analysing the presence or absence of edges and textual data is often discarded. However, all communication networks actually come with textual data on the edges. In order to take into account this specificity, we consider in this paper networks for which two nodes are linked if and only if they share textual data. We introduce a deep latent variable model allowing embedded topics to be handled called ETSBM to simultaneously perform clustering on the nodes while modelling the topics used between the different clusters. ETSBM extends both the stochastic block model (SBM) and the embedded topic model (ETM) which are core models for studying networks and corpora, respectively. The inference is done using a variational-Bayes expectation-maximisation algorithm combined with a stochastic gradient descent. The methodology is evaluated on synthetic data and on a real world dataset.

cs.SI↗

arXiv2023

Are labels informative in semi-supervised learning? -- Estimating and leveraging the missing-data mechanism

Semi-supervised learning is a powerful technique for leveraging unlabeled data to improve machine learning models, but it can be affected by the presence of ``informative'' labels, which occur when some classes are more likely to be labeled than others. In the missing data literature, such labels are called missing not at random. In this paper, we propose a novel approach to address this issue by estimating the missing-data mechanism and using inverse propensity weighting to debias any SSL algorithm, including those using data augmentation. We also propose a likelihood ratio test to assess whether or not labels are indeed informative. Finally, we demonstrate the performance of the proposed methods on different datasets, in particular on two medical datasets for which we design pseudo-realistic missing data scenarios.

stat.ML↗

arXiv2022

Generalised Mutual Information for Discriminative Clustering

In the last decade, recent successes in deep clustering majorly involved the mutual information (MI) as an unsupervised objective for training neural networks with increasing regularisations. While the quality of the regularisations have been largely discussed for improvements, little attention has been dedicated to the relevance of MI as a clustering objective. In this paper, we first highlight how the maximisation of MI does not lead to satisfying clusters. We identified the Kullback-Leibler divergence as the main reason of this behaviour. Hence, we generalise the mutual information by changing its core distance, introducing the generalised mutual information (GEMINI): a set of metrics for unsupervised neural network training. Unlike MI, some GEMINIs do not require regularisations when training. Some of these metrics are geometry-aware thanks to distances or kernels in the data space. Finally, we highlight that GEMINIs can automatically select a relevant number of clusters, a property that has been little studied in deep clustering context where the number of clusters is a priori unknown.

stat.ML↗

arXiv2021

Active Speaker Detection as a Multi-Objective Optimization with Uncertainty-based Multimodal Fusion

It is now well established from a variety of studies that there is a significant benefit from combining video and audio data in detecting active speakers. However, either of the modalities can potentially mislead audiovisual fusion by inducing unreliable or deceptive information. This paper outlines active speaker detection as a multi-objective learning problem to leverage best of each modalities using a novel self-attention, uncertainty-based multimodal fusion scheme. Results obtained show that the proposed multi-objective learning architecture outperforms traditional approaches in improving both mAP and AUC scores. We further demonstrate that our fusion strategy surpasses, in active speaker detection, other modality fusion methods reported in various disciplines. We finally show that the proposed method significantly improves the state-of-the-art on the AVA-ActiveSpeaker dataset.

cs.SD↗

arXiv2021

Hierarchical clustering with discrete latent variable models and the integrated classification likelihood

Finding a set of nested partitions of a dataset is useful to uncover relevant structure at different scales, and is often dealt with a data-dependent methodology. In this paper, we introduce a general two-step methodology for model-based hierarchical clustering. Considering the integrated classification likelihood criterion as an objective function, this work applies to every discrete latent variable models (DLVMs) where this quantity is tractable. The first step of the methodology involves maximizing the criterion with respect to the partition. Addressing the known problem of sub-optimal local maxima found by greedy hill climbing heuristics, we introduce a new hybrid algorithm based on a genetic algorithm efficiently exploring the space of solutions. The resulting algorithm carefully combines and merges different solutions, and allows the joint inference of the number $K$ of clusters as well as the clusters themselves. Starting from this natural partition, the second step of the methodology is based on a bottom-up greedy procedure to extract a hierarchy of clusters. In a Bayesian context, this is achieved by considering the Dirichlet cluster proportion prior parameter $α$ as a regularization term controlling the granularity of the clustering. A new approximation of the criterion is derived as a log-linear function of $α$, enabling a simple functional form of the merge decision criterion. This second step allows the exploration of the clustering at coarser scales. The proposed approach is compared with existing strategies on simulated as well as real settings, and its results are shown to be particularly relevant. A reference implementation of this work is available in the R package greed accompanying the paper.

stat.CO↗

arXiv2021

Co-clustering of time-dependent data via Shape Invariant Model

Multivariate time-dependent data, where multiple features are observed over time for a set of individuals, are increasingly widespread in many application domains. To model these data we need to account for relations among both time instants and variables and, at the same time, for subjects heterogeneity. We propose a new co-clustering methodology for clustering individuals and variables simultaneously that is designed to handle both functional and longitudinal data. Our approach borrows some concepts from the curve registration framework by embedding the Shape Invariant Model in the Latent Block Model, estimated via a suitable modification of the SEM-Gibbs algorithm. The resulting procedure allows for several user-defined specifications of the notion of cluster that could be chosen on substantive grounds and provides parsimonious summaries of complex longitudinal or functional data by partitioning data matrices into homogeneous blocks.

stat.ME↗

arXiv2021

Unobserved classes and extra variables in high-dimensional discriminant analysis

In supervised classification problems, the test set may contain data points belonging to classes not observed in the learning phase. Moreover, the same units in the test data may be measured on a set of additional variables recorded at a subsequent stage with respect to when the learning sample was collected. In this situation, the classifier built in the learning phase needs to adapt to handle potential unknown classes and the extra dimensions. We introduce a model-based discriminant approach, Dimension-Adaptive Mixture Discriminant Analysis (D-AMDA), which can detect unobserved classes and adapt to the increasing dimensionality. Model estimation is carried out via a full inductive approach based on an EM algorithm. The method is then embedded in a more general framework for adaptive variable selection and classification suitable for data of large dimensions. A simulation study and an artificial experiment related to classification of adulterated honey samples are used to validate the ability of the proposed framework to deal with complex situations.

stat.ME↗

arXiv2020

A Bayesian Fisher-EM algorithm for discriminative Gaussian subspace clustering

High-dimensional data clustering has become and remains a challenging task for modern statistics and machine learning, with a wide range of applications. We consider in this work the powerful discriminative latent mixture model, and we extend it to the Bayesian framework. Modeling data as a mixture of Gaussians in a low-dimensional discriminative subspace, a Gaussian prior distribution is introduced over the latent group means and a family of twelve submodels are derived considering different covariance structures. Model inference is done with a variational EM algorithm, while the discriminative subspace is estimated via a Fisher-step maximizing an unsupervised Fisher criterion. An empirical Bayes procedure is proposed for the estimation of the prior hyper-parameters, and an integrated classification likelihood criterion is derived for selecting both the number of clusters and the submodel. The performances of the resulting Bayesian Fisher-EM algorithm are investigated in two thorough simulated scenarios, regarding both dimensionality as well as noise and assessing its superiority with respect to state-of-the-art Gaussian subspace clustering models. In addition to standard real data benchmarks, an application to single image denoising is proposed, displaying relevant results. This work comes with a reference implementation for the R software in the FisherEM package accompanying the paper.

stat.ME↗

arXiv2020

Greedy clustering of count data through a mixture of multinomial PCA

Count data is becoming more and more ubiquitous in a wide range of applications, with datasets growing both in size and in dimension. In this context, an increasing amount of work is dedicated to the construction of statistical models directly accounting for the discrete nature of the data. Moreover, it has been shown that integrating dimension reduction to clustering can drastically improve performance and stability. In this paper, we rely on the mixture of multinomial PCA, a mixture model for the clustering of count data, also known as the probabilistic clustering-projection model in the literature. Related to the latent Dirichlet allocation model, it offers the flexibility of topic modeling while being able to assign each observation to a unique cluster. We introduce a greedy clustering algorithm, where inference and clustering are jointly done by mixing a classification variational expectation maximization algorithm, with a branch & bound like strategy on a variational lower bound. An integrated classification likelihood criterion is derived for model selection, and a thorough study with numerical experiments is proposed to assess both the performance and robustness of the method. Finally, we illustrate the qualitative interest of the latter in a real-world application, for the clustering of anatomopathological medical reports, in partnership with expert practitioners from the Institut Curie hospital.

stat.ME↗

arXiv2019

Exact Dimensionality Selection for Bayesian PCA

We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high-dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a normal-gamma prior distribution. In this context, we exhibit a closed-form expression of the marginal likelihood which allows to infer an optimal number of components. We also propose a heuristic based on the expected shape of the marginal likelihood curve in order to choose the hyperparameters. In non-asymptotic frameworks, we show on simulated data that this exact dimensionality selection approach is competitive with both Bayesian and frequentist state-of-the-art methods.

stat.ME↗