arXiv subjects

Christophe Biernacki

Publications and source records attributed to Christophe Biernacki.

11 recordsLinked to original sources

arXiv2026

From Unsupervised to Guided Clustering: A Variational Implementation

Clustering is viewed as an unsupervised technique, but in practice it requires guidance to uncover meaningful structures. We formalize this with guided clustering, a paradigm that uses a guiding variable to steer the discovery process, and introduce the Guided Clustering Variational Autoencoder (GCVAE) as its deep generative realization. GCVAE learns a latent space structured as a Gaussian Mixture Model by optimizing a variational objective that forces the representation to be maximally informative about the guiding variable. This framework allows the resulting clustering to be reoriented by changing the guiding variable, yielding clusters that are meaningful for the specified context. Experiments on public (MNIST-SVHN) and proprietary connected health devices data demonstrate GCVAE's ability to discover coherent and task-relevant clusters in complex settings.

stat.ME↗

arXiv2024

Comparative study of clustering models for multivariate time series from connected medical devices

In healthcare, patient data is often collected as multivariate time series, providing a comprehensive view of a patient's health status over time. While this data can be sparse, connected devices may enhance its frequency. The goal is to create patient profiles from these time series. In the absence of labels, a predictive model can be used to predict future values while forming a latent cluster space, evaluated based on predictive performance. We compare two models on Withing's datasets, M AGMAC LUST which clusters entire time series and DGM${}^2$ which allows the group affiliation of an individual to change over time (dynamic clustering).

cs.LG↗

arXiv2023

Model-based Clustering with Missing Not At Random Data

Model-based unsupervised learning, as any learning task, stalls as soon as missing data occurs. This is even more true when the missing data are informative, or said missing not at random (MNAR). In this paper, we propose model-based clustering algorithms designed to handle very general types of missing data, including MNAR data. To do so, we introduce a mixture model for different types of data (continuous, count, categorical and mixed) to jointly model the data distribution and the MNAR mechanism, remaining vigilant to the relative degrees of freedom of each. Several MNAR models are discussed, for which the cause of the missingness can depend on both the values of the missing variable themselves and on the class membership. However, we focus on a specific MNAR model, called MNARz, for which the missingness only depends on the class membership. We first underline its ease of estimation, by showing that the statistical inference can be carried out on the data matrix concatenated with the missing mask considering finally a standard MAR mechanism. Consequently, we propose to perform clustering using the Expectation Maximization algorithm, specially developed for this simplified reinterpretation. Finally, we assess the numerical performances of the proposed methods on synthetic data and on the real medical registry TraumaBase as well.

stat.ML↗

arXiv2022

An iterative clustering algorithm for the Contextual Stochastic Block Model with optimality guarantees

Real-world networks often come with side information that can help to improve the performance of network analysis tasks such as clustering. Despite a large number of empirical and theoretical studies conducted on network clustering methods during the past decade, the added value of side information and the methods used to incorporate it optimally in clustering algorithms are relatively less understood. We propose a new iterative algorithm to cluster networks with side information for nodes (in the form of covariates) and show that our algorithm is optimal under the Contextual Symmetric Stochastic Block Model. Our algorithm can be applied to general Contextual Stochastic Block Models and avoids hyperparameter tuning in contrast to previously proposed methods. We confirm our theoretical results on synthetic data experiments where our algorithm significantly outperforms other methods, and show that it can also be applied to signed graphs. Finally we demonstrate the practical interest of our method on real data.

stat.ML↗

arXiv2021

Clustering multilayer graphs with missing nodes

Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise naturally in many contexts including biological and social networks. Clustering is a fundamental problem in network analysis where the goal is to regroup nodes with similar connectivity profiles. In the past decade, various clustering methods have been extended from the unilayer setting to multilayer graphs in order to incorporate the information provided by each layer. While most existing works assume - rather restrictively - that all layers share the same set of nodes, we propose a new framework that allows for layers to be defined on different sets of nodes. In particular, the nodes not recorded in a layer are treated as missing. Within this paradigm, we investigate several generalizations of well-known clustering methods in the complete setting to the incomplete one and prove some consistency results under the Multi-Layer Stochastic Block Model assumption. Our theoretical results are complemented by thorough numerical comparisons between our proposed algorithms on synthetic data, and also on real datasets, thus highlighting the promising behaviour of our methods in various settings.

stat.ML↗

arXiv2020

Simultaneous semi-parametric estimation of clustering and regression

We investigate the parameter estimation of regression models with fixed group effects, when the group variable is missing while group related variables are available. This problem involves clustering to infer the missing group variable based on the group related variables, and regression to build a model on the target variable given the group and eventually additional variables. Thus, this problem can be formulated as the joint distribution modeling of the target and of the group related variables. The usual parameter estimation strategy for this joint model is a two-step approach starting by learning the group variable (clustering step) and then plugging in its estimator for fitting the regression model (regression step). However, this approach is suboptimal (providing in particular biased regression estimates) since it does not make use of the target variable for clustering. Thus, we claim for a simultaneous estimation approach of both clustering and regression, in a semi-parametric framework. Numerical experiments illustrate the benefits of our proposition by considering wide ranges of distributions and regression models. The relevance of our new method is illustrated on real data dealing with problems associated with high blood pressure prevention.

stat.ME↗

arXiv2019

Feature quantization for parsimonious and interpretable predictive models

For regulatory and interpretability reasons, logistic regression is still widely used. To improve prediction accuracy and interpretability, a preprocessing step quantizing both continuous and categorical data is usually performed: continuous features are discretized and, if numerous, levels of categorical features are grouped. An even better predictive accuracy can be reached by embedding this quantization estimation step directly into the predictive estimation step itself. But doing so, the predictive loss has to be optimized on a huge set. To overcome this difficulty, we introduce a specific two-step optimization strategy: first, the optimization problem is relaxed by approximating discontinuous quantization functions by smooth functions; second, the resulting relaxed optimization problem is solved via a particular neural network. The good performances of this approach, which we call glmdisc, are illustrated on simulated and real data from the UCI library and Crédit Agricole Consumer Finance (a major European historic player in the consumer credit market).

stat.ME↗

arXiv2019

Réintégration des refusés en Credit Scoring

The granting process of all credit institutions rejects applicants who seem risky regarding the repayment of their debt. A credit score is calculated and associated with a cut-off value beneath which an applicant is rejected. Developing a new score implies having a learning dataset in which the response variable good/bad borrower is known, so that rejects are de facto excluded from the learning process. We first introduce the context and some useful notations. Then we formalize if this particular sampling has consequences on the score's relevance. Finally, we elaborate on methods that use not-financed clients' characteristics and conclude that none of these methods are satisfactory in practice using data from Crédit Agricole Consumer Finance. ----- Un système d'octroi de crédit peut refuser des demandes de prêt jugées trop risquées. Au sein de ce système, le score de crédit fournit une valeur mesurant un risque de défaut, valeur qui est comparée à un seuil d'acceptabilité. Ce score est construit exclusivement sur des données de clients financés, contenant en particulier l'information `bon ou mauvais payeur', alors qu'il est par la suite appliqué à l'ensemble des demandes. Un tel score est-il statistiquement pertinent ? Dans cette note, nous précisons et formalisons cette question et étudions l'effet de l'absence des non-financés sur les scores élaborés. Nous présentons ensuite des méthodes pour réintégrer les non-financés et concluons sur leur inefficacité en pratique, à partir de données issues de Crédit Agricole Consumer Finance.

econ.GN↗

arXiv2015

Model-based clustering of Gaussian copulas for mixed data

Clustering task of mixed data is a challenging problem. In a probabilistic framework, the main difficulty is due to a shortage of conventional distributions for such data. In this paper, we propose to achieve the mixed data clustering with a Gaussian copula mixture model, since copulas, and in particular the Gaussian ones, are powerful tools for easily modelling the distribution of multivariate variables. Indeed, considering a mixing of continuous, integer and ordinal variables (thus all having a cumulative distribution function), this copula mixture model defines intra-component dependencies similar to a Gaussian mixture, so with classical correlation meaning. Simultaneously, it preserves standard margins associated to continuous, integer and ordered features, namely the Gaussian, the Poisson and the ordered multinomial distributions. As an interesting by-product, the proposed mixture model generalizes many well-known ones and also provides tools of visualization based on the parameters. At a practical level, the Bayesian inference is retained and it is achieved with a Metropolis-within-Gibbs sampler. Experiments on simulated and real data sets finally illustrate the expected advantages of the proposed model for mixed data: flexible and meaningful parametrization combined with visualization features.

stat.ME↗

arXiv2014

Model-based clustering for conditionally correlated categorical data

An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and intra-dependent blocks, in order to consider the main intra-class correlations. The dependency between variables grouped inside the same block of a class is taken into account by mixing two extreme distributions, which are respectively the independence and the maximum dependency. When the variables are dependent given the class, this approach is expected to reduce the biases of the latent class model. Indeed, it produces a meaningful dependency model with only a few additional parameters. The parameters are estimated, by maximum likelihood, by means of an EM algorithm. Moreover, a Gibbs sampler is used for model selection in order to overcome the computational intractability of the combinatorial problems involved by the block structure search. Two applications on medical and biological data sets show the relevance of this new model. The results strengthen the view that this model is meaningful and that it reduces the biases induced by the conditional independence assumption of the latent class model.

stat.CO↗

arXiv2014

Finite mixture model of conditional dependencies modes to cluster categorical data

We propose a parsimonious extension of the classical latent class model to cluster categorical data by relaxing the class conditional independence assumption. Under this new mixture model, named Conditional Modes Model, variables are grouped into conditionally independent blocks. The corresponding block distribution is a parsimonious multinomial distribution where the few free parameters correspond to the most likely modality crossings, while the remaining probability mass is uniformly spread over the other modality crossings. Thus, the proposed model allows to bring out the intra-class dependency between variables and to summarize each class by a few characteristic modality crossings. The model selection is performed via a Metropolis-within-Gibbs sampler to overcome the computational intractability of the block structure search. As this approach involves the computation of the integrated complete-data likelihood, we propose a new method (exact for the continuous parameters and approximated for the discrete ones) which avoids the biases of the \textsc{bic} criterion pointed out by our experiments. Finally, the parameters are only estimated for the best model via an \textsc{em} algorithm. The characteristics of the new model are illustrated on simulated data and on two biological data sets. These results strengthen the idea that this simple model allows to reduce biases involved by the conditional independence assumption and gives meaningful parameters. Both applications were performed with the R package \texttt{CoModes}

stat.ME↗