arXiv subjects

Pierre Lafaye de Micheaux

Publications and source records attributed to Pierre Lafaye de Micheaux.

21 records · Page 2Linked to original sources

arXiv2018

A uniform $L^1$ law of large numbers for functions of i.i.d. random variables that are translated by a consistent estimator

We develop a new $L^1$ law of large numbers where the $i$-th summand is given by a function $h(\cdot)$ evaluated at $X_i - θ_n$, and where $θ_n \circeq θ_n(X_1,X_2,\ldots,X_n)$ is an estimator converging in probability to some parameter $θ\in \mathbb{R}$. Under broad technical conditions, the convergence is shown to hold uniformly in the set of estimators interpolating between $θ$ and another consistent estimator $θ_n^{\star}$. Our main contribution is the treatment of the case where $|h|$ blows up at $0$, which is not covered by standard uniform laws of large numbers.

math.PR↗

arXiv2017

A Unified Parallel Algorithm for Regularized Group PLS Scalable to Big Data

Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocs of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of observations and in presence of high collinearity between variables. Different sparse versions of PLS have been developed to integrate multiple data sets while simultaneously selecting the contributing variables. Sparse modelling is a key factor in obtaining better estimators and identifying associations between multiple data sets. The cornerstone of the sparsity version of PLS methods is the link between the SVD of a matrix (constructed from deflated versions of the original matrices of data) and least squares minimisation in linear regression. We present here an accurate description of the most popular PLS methods, alongside their mathematical proofs. A unified algorithm is proposed to perform all four types of PLS including their regularised versions. Various approaches to decrease the computation time are offered, and we show how the whole procedure can be scalable to big data sets.

stat.ML↗

arXiv2010

Temporal and Spatial Independent Component Analysis for fMRI data sets embedded in a R package

For statistical analysis of functional Magnetic Resonance Imaging (fMRI) data sets, we propose a data-driven approach based on Independent Component Analysis (ICA) implemented in a new version of the AnalyzeFMRI R package. For fMRI data sets, spatial dimension being much greater than temporal dimension, spatial ICA is the tractable approach generally proposed. However, for some neuroscientific applications, temporal independence of source signals can be assumed and temporal ICA becomes then an attracting exploratory technique. In this work, we use a classical linear algebra result ensuring the tractability of temporal ICA. We report several experiments on synthetic data and real MRI data sets that demonstrate the potential interest of our R package.

stat.CO↗