arXiv subjects

Mélanie Blazère

Publications and source records attributed to Mélanie Blazère.

4 recordsLinked to original sources

arXiv2025

Covariance constraints for stochastic inverse problems of computer models

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and such problems are increasingly examined in parametric Bayesian contexts where the parameters of the targeted input distributions are affected by epistemic uncertainties. With the aim of improving the meaningfulness of solutions found by statistical algorithms -- in the sense that forward simulations based on such solutions must lead to relevant observables -- we derive new prior constraints using the principles of global sensitivity analysis and information theory. Primarily formalized as constraints on covariances in Gaussian linear or linearizable situations, they reflect the idea that the solution should explain most of the observable uncertainty, while the model noise remains a secondary factor of this uncertainty. Simulated experiments highlight that, when injected into stochastic inversion algorithms, these constraints can indeed limit the influence of model noise on the result. They provide hope for future extensions in more general frameworks, for example through the use of linear Gaussian mixtures.

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arXiv2014

A unified framework for the study of the PLS estimator's properties

In this paper we propose a new approach to study the properties of the Partial Least Squares (PLS) estimator. This approach relies on the link between PLS and discrete orthogonal polynomials. Indeed many important PLS objects can be expressed in terms of some specific discrete orthogonal polynomials, called the residual polynomials. Based on the explicit analytical expression we have stated for these polynomials in terms of signal and noise, we provide a new framework for the study of PLS. Furthermore, we show that this new approach allows to simplify and retreive independent proofs of many classical results (proved earlier by different authors using various approaches and tools). This general and unifying approach also sheds new light on PLS and helps to gain insight on its properties.

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arXiv2014

PLS: a new statistical insight through the prism of orthogonal polynomials

Partial Least Square (PLS) is a dimension reduction method used to remove multicollinearities in a regression model. However contrary to Principal Components Analysis (PCA) the PLS components are also choosen to be optimal for predicting the response $Y$. In this paper we provide a new and explicit formula for the residuals. We show that the residuals are completely determined by the spectrum of the design matrix and by the noise on the observations. Because few are known on the behaviour of the PLS components we also investigate their statistical properties in a regression context. New results on regression and prediction error for PLS are stated under the assumption of a low variance of the noise.

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arXiv2014

Group Lasso for generalized linear models in high dimension

Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good estimation of the regression parameter. This sparsity assumption as well as a block structuration of the covariates into groups with similar modes of behavior is for example quite natural in genomics. A huge amount of scientific literature exists for Gaussian linear models including the Lasso estimator and also the Group Lasso estimator which promotes group sparsity under an a priori knowledge of the groups. We extend this Group Lasso procedure to generalized linear models and we study the properties of this estimator for sparse high-dimensional generalized linear models to find convergence rates. We provide oracle inequalities for the prediction and estimation error under assumptions on the covariables and under a condition on the design matrix. We show the ability of this estimator to recover good sparse approximation of the true model. At last we extend these results to the case of an Elastic net penalty and we apply them to the so-called Poisson regression case which has not been studied in this context contrary to the logistic regression.

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