Randal Douc (CITI, Telecom SudParis) 

Amphi C2.0.37

Boost your favorite Markov Chain Monte Carlo sampler using Kac's theorem: the Kick-Kac teleportation algorithm

Résumé : TThe present paper focuses on the problem of sampling from a given target distribution π defined on some general state space. To this end, we introduce a novel class of non-reversible Markov chains, each chain being defined on an extended state space and having an invariant probability measure admitting π as a marginal distribution. The proposed methodology is inspired by a new formulation of Kac's theorem and allows global and local dynamics to be smoothly combined. Under mild conditions, the corresponding Markov transition kernel can be shown to be irreducible and Harris recurrent. In addition, we establish that geometric ergodicity holds under appropriate conditions on the global and local dynamics. Finally, we illustrate numerically the use of the proposed method and its potential benefits in comparison to existing Markov chain Monte Carlo (MCMC) algorithms. Joint work with Alain Durmus (Ecole Polytechnique), Aurélien Enfroy (Orsay), Jimmy Olsson (KTH).

Margaux Zaffran  (CMAP, Ecole polytechnique) 

Amphi C2.0.37

Uncertainty quantification in presence of missing values

Résumé : Uncertainty quantification of predictive models is crucial in decision-making problems. To this purpose, quantile regression can be used to construct prediction intervals, but its validity relies on asymptotic and regularity conditions, and depends on the underlying model. Conformal prediction (CP) is a theoretically grounded framework for constructing prediction intervals with finite sample distribution-free marginal coverage guarantee that holds under the assumption that training and test points are exchangeable. The presence of missing values in real data brings additional challenges to uncertainty quantification. Despite an abundant literature on missing data, as far as we know, there is no work studying the quantification of uncertainty in predictive models.

In this work, we first show that, for almost all imputations, a universally consistent quantile regression algorithm trained on the imputed data is Bayes optimal for the pinball risk. In the finite-sample regime, we show that, for almost all imputations and missing values mechanisms, the imputed data set is exchangeable. Thus, CP properties still hold and marginal guarantees are met. Nevertheless, we emphasize that the average coverage varies depending on the pattern of missing values: it tends to construct prediction intervals that often under-cover the response conditional on a given missing pattern. After theoretically studying the case of a linear model, we propose a methodology to achieve approximate conditional guarantees conditional on the 2^d patterns of missing values, where d is the data dimension. We assess its improved performance on synthetic experiments.

Marina Gomtsyan (MIA Paris-Saclay, AgroParisTech) 

Amphi C2.0.37

Variable selection in sparse GLARMA models

Résumé : We propose a novel and efficient iterative two-stage variable selection approach for univariate and multivariate sparse GLARMA models, which can be used for modelling discrete-valued time series. Our approach consists in iteratively combining two steps: the estimation of the autoregressive moving average (ARMA) coefficients of multivariate GLARMA models and the variable selection in the coefficients of the Generalized Linear Model (GLM) part of the model performed by regularized methods. We explain how to implement our approach efficiently. Then we assess the performance of our methodology using synthetic data and compare it with alternative methods. Finally, we illustrate it on RNA-Seq data resulting from polyribosome profiling to determine translational status for all mRNAs in germinating seeds. Our approach is implemented in GlarmaVarSel and MultiGlarmaVarSel R packages for univariate and multivariate settings, which are available on the CRAN. Our methodology is very attractive since it benefits from a low computational load and is able to outperform the other methods for recovering the null and non-null coefficients.