Sylvain Arlot

Bio: Sylvain Arlot is an academic researcher from Département de Mathématiques. The author has contributed to research in topics: Model selection & Estimator. The author has an hindex of 25, co-authored 58 publications receiving 6493 citations. Previous affiliations of Sylvain Arlot include Université Paris-Saclay & École Normale Supérieure.

A survey of cross-validation procedures for model selection

Abstract: Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of cross-validation procedures. This survey intends to relate these results to the most recent advances of model selection theory, with a particular emphasis on distinguishing empirical statements from rigorous theoretical results. As a conclusion, guidelines are provided for choosing the best cross-validation procedure according to the particular features of the problem in hand.

A survey of cross-validation procedures for model selection

Abstract: Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of cross-validation procedures. This survey intends to relate these results to the most recent advances of model selection theory, with a particular emphasis on distinguishing empirical statements from rigorous theoretical results. As a conclusion, guidelines are provided for choosing the best cross-validation procedure according to the particular features of the problem in hand.

Data-driven Calibration of Penalties for Least-Squares Regression

Abstract: Penalization procedures often suffer from their dependence on multiplying factors, whose optimal values are either unknown or hard to estimate from data. We propose a completely data-driven calibration algorithm for these parameters in the least-squares regression framework, without assuming a particular shape for the penalty. Our algorithm relies on the concept of minimal penalty, recently introduced by Birge and Massart (2007) in the context of penalized least squares for Gaussian homoscedastic regression. On the positive side, the minimal penalty can be evaluated from the data themselves, leading to a data-driven estimation of an optimal penalty which can be used in practice; on the negative side, their approach heavily relies on the homoscedastic Gaussian nature of their stochastic framework. The purpose of this paper is twofold: stating a more general heuristics for designing a data-driven penalty (the slope heuristics) and proving that it works for penalized least-squares regression with a random design, even for heteroscedastic non-Gaussian data. For technical reasons, some exact mathematical results will be proved only for regressogram bin-width selection. This is at least a first step towards further results, since the approach and the method that we use are indeed general.

Cross-validation

Abstract: This text is a survey on cross-validation We define all classical cross-validation procedures, and we study their properties for two different goals: estimating the risk of a given estimator, and selecting the best estimator among a given family For the risk estimation problem, we compute the bias (which can also be corrected) and the variance of cross-validation methods For estimator selection, we first provide a first-order analysis (based on expectations) Then, we explain how to take into account second-order terms (from variance computations, and by taking into account the usefulness of overpenalization) This allows, in the end, to provide some guidelines for choosing the best cross-validation method for a given learning problem

A Kernel Multiple Change-point Algorithm via Model Selection

Abstract: We tackle the change-point problem with data belonging to a general set. We build a penalty for choosing the number of change-points in the kernel-based method of Harchaoui and Cappe (2007). This penalty generalizes the one proposed by Lebarbier (2005) for one-dimensional signals. We prove a non-asymptotic oracle inequality for the proposed method, thanks to a new concentration result for some function of Hilbert-space valued random variables. Experiments on synthetic data illustrate the accuracy of our method, showing that it can detect changes in the whole distribution of data, even when the mean and variance are constant.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

Abstract: From the Publisher: The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

A survey of cross-validation procedures for model selection

Abstract: Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of cross-validation procedures. This survey intends to relate these results to the most recent advances of model selection theory, with a particular emphasis on distinguishing empirical statements from rigorous theoretical results. As a conclusion, guidelines are provided for choosing the best cross-validation procedure according to the particular features of the problem in hand.

A survey of cross-validation procedures for model selection

Abstract: Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of cross-validation procedures. This survey intends to relate these results to the most recent advances of model selection theory, with a particular emphasis on distinguishing empirical statements from rigorous theoretical results. As a conclusion, guidelines are provided for choosing the best cross-validation procedure according to the particular features of the problem in hand.

Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC

Abstract: Leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the posterior simulations of the parameter values. LOO and WAIC have various advantages over simpler estimates of predictive error such as AIC and DIC but are less used in practice because they involve additional computational steps. Here we lay out fast and stable computations for LOO and WAIC that can be performed using existing simulation draws. We introduce an efficient computation of LOO using Pareto-smoothed importance sampling (PSIS), a new procedure for regularizing importance weights. Although WAIC is asymptotically equal to LOO, we demonstrate that PSIS-LOO is more robust in the finite case with weak priors or influential observations. As a byproduct of our calculations, we also obtain approximate standard errors for estimated predictive errors and for comparing of predictive errors between two models. We implement the computations in an R package called 'loo' and demonstrate using models fit with the Bayesian inference package Stan.