arXiv subjects

Cathy Maugis-Rabusseau

Publications and source records attributed to Cathy Maugis-Rabusseau.

7 recordsLinked to original sources

arXiv2023

Selective inference after convex clustering with $\ell_1$ penalization

Classical inference methods notoriously fail when applied to data-driven test hypotheses or inference targets. Instead, dedicated methodologies are required to obtain statistical guarantees for these selective inference problems. Selective inference is particularly relevant post-clustering, typically when testing a difference in mean between two clusters. In this paper, we address convex clustering with $\ell_1$ penalization, by leveraging related selective inference tools for regression, based on Gaussian vectors conditioned to polyhedral sets. In the one-dimensional case, we prove a polyhedral characterization of obtaining given clusters, than enables us to suggest a test procedure with statistical guarantees. This characterization also allows us to provide a computationally efficient regularization path algorithm. Then, we extend the above test procedure and guarantees to multi-dimensional clustering with $\ell_1$ penalization, and also to more general multi-dimensional clusterings that aggregate one-dimensional ones. With various numerical experiments, we validate our statistical guarantees and we demonstrate the power of our methods to detect differences in mean between clusters. Our methods are implemented in the R package poclin.

stat.ME↗

arXiv2017

Variable selection in model-based clustering and discriminant analysis with a regularization approach

Relevant methods of variable selection have been proposed in model-based clustering and classification. These methods are making use of backward or forward procedures to define the roles of the variables. Unfortunately, these stepwise procedures are terribly slow and make these variable selection algorithms inefficient to treat large data sets. In this paper, an alternative regularization approach of variable selection is proposed for model-based clustering and classification. In this approach, the variables are first ranked with a lasso-like procedure in order to avoid painfully slow stepwise algorithms. Thus, the variable selection methodology of Maugis et al (2009b) can be efficiently applied on high-dimensional data sets.

stat.CO↗

arXiv2017

Clustering transformed compositional data using K-means, with applications in gene expression and bicycle sharing system data

Although there is no shortage of clustering algorithms proposed in the literature, the question of the most relevant strategy for clustering compositional data (i.e., data made up of profiles, whose rows belong to the simplex) remains largely unexplored in cases where the observed value of an observation is equal or close to zero for one or more samples. This work is motivated by the analysis of two sets of compositional data, both focused on the categorization of profiles but arising from considerably different applications: (1) identifying groups of co-expressed genes from high-throughput RNA sequencing data, in which a given gene may be completely silent in one or more experimental conditions; and (2) finding patterns in the usage of stations over the course of one week in the Velib' bicycle sharing system in Paris, France. For both of these applications, we focus on the use of appropriately chosen data transformations, including the Centered Log Ratio and a novel extension we propose called the Log Centered Log Ratio, in conjunction with the K-means algorithm. We use a nonasymptotic penalized criterion, whose penalty is calibrated with the slope heuristics, to select the number of clusters present in the data. Finally, we illustrate the performance of this clustering strategy, which is implemented in the Bioconductor package coseq, on both the gene expression and bicycle sharing system data.

math.ST↗

arXiv2016

Parameter recovery in two-component contamination mixtures: the $\mathbb{L}^2$ strategy

In this paper, we consider a parametric density contamination model. We work with a sample of i.i.d. data with a common density, $f^\star =(1-\lambda^\star) \phi + \lambda^\star \phi(.-\mu^\star)$, where the shape $\phi$ is assumed to be known. We establish the optimal rates of convergence for the estimation of the mixture parameters $(\lambda^\star,\mu^\star)$. In particular, we prove that the classical parametric rate $1/\sqrt{n}$ cannot be reached when at least one of these parameters is allowed to tend to $0$ with $n$.

math.ST↗

arXiv2015

Multidimensional two-component Gaussian mixtures detection

Let $(X\_1,\ldots,X\_n)$ be a $d$-dimensional i.i.d sample from a distribution with density $f$. The problem of detection of a two-component mixture is considered. Our aim is to decide whether $f$ is the density of a standard Gaussian random $d$-vector ($f=\phi\_d$) against $f$ is a two-component mixture: $f=(1-\varepsilon)\phi\_d +\varepsilon \phi\_d (.-\mu)$ where $(\varepsilon,\mu)$ are unknown parameters. Optimal separation conditions on $\varepsilon, \mu, n$ and the dimension $d$ are established, allowing to separate both hypotheses with prescribed errors. Several testing procedures are proposed and two alternative subsets are considered.

math.ST↗

arXiv2013

Comparing Model Selection and Regularization Approaches to Variable Selection in Model-Based Clustering

We compare two major approaches to variable selection in clustering: model selection and regularization. Based on previous results, we select the method of Maugis et al. (2009b), which modified the method of Raftery and Dean (2006), as a current state of the art model selection method. We select the method of Witten and Tibshirani (2010) as a current state of the art regularization method. We compared the methods by simulation in terms of their accuracy in both classification and variable selection. In the first simulation experiment all the variables were conditionally independent given cluster membership. We found that variable selection (of either kind) yielded substantial gains in classification accuracy when the clusters were well separated, but few gains when the clusters were close together. We found that the two variable selection methods had comparable classification accuracy, but that the model selection approach had substantially better accuracy in selecting variables. In our second simulation experiment, there were correlations among the variables given the cluster memberships. We found that the model selection approach was substantially more accurate in terms of both classification and variable selection than the regularization approach, and that both gave more accurate classifications than $K$-means without variable selection.

stat.AP↗

arXiv2013

Non-asymptotic detection of two-component mixtures with unknown means

This work is concerned with the detection of a mixture distribution from a $\mathbb{R}$-valued sample. Given a sample $X_1,\dots,X_n$ and an even density $\phi$, our aim is to detect whether the sample distribution is $\phi(\cdot-\mu)$ for some unknown mean $\mu$, or is defined as a two-component mixture based on translations of $\phi$. We propose a procedure which is based on several spacings of the order statistics, which provides a level-$\alpha$ test for all $n$. Our test is therefore a multiple testing procedure and we prove from a theoretical and practical point of view that it automatically adapts to the proportion of the mixture and to the difference of the means of the two components of the mixture under the alternative. From a theoretical point of view, we prove the optimality of the power of our procedure in various situations. A simulation study shows the good performances of our test compared with several classical procedures.

math.ST↗