Related papers: Simulating Gaussian vectors via randomized dimensi…

We introduce a new discriminant analysis method (Empirical Discriminant Analysis or EDA) for binary classification in machine learning. Given a dataset of feature vectors, this method defines an empirical feature map transforming the…

In this paper, we present a new estimator of the mean of a random vector, computed by applying some threshold function to the norm. Non asymptotic dimension-free almost sub-Gaussian bounds are proved under weak moment assumptions, using…

For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…

The computation of Gaussian orthant probabilities has been extensively studied for low-dimensional vectors. Here, we focus on the high-dimensional case and we present a two-step procedure relying on both deterministic and stochastic…

This paper presents an algorithm to simulate Gaussian random vectors whose precision matrix can be expressed as a polynomial of a sparse matrix. This situation arises in particular when simulating Gaussian Markov random fields obtained by…

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish lower bounds on the rates of convergence of the estimators of the…

We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…

High covariate dimensionality is increasingly occurrent in model estimation, and existing techniques to address this issue typically require sparsity or discrete heterogeneity of the \emph{unobservable} parameter vector. However, neither…

In this paper we present a novel analysis of variance Gaussian process (ANOVA-GP) emulator for models governed by partial differential equations (PDEs) with high-dimensional random inputs. Gaussian process (GP) is a widely used surrogate…

Rare event probability estimation is an important topic in reliability analysis. Stochastic methods, such as importance sampling, have been developed to estimate such probabilities but they often fail in high dimension. In this paper, we…

We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the…

Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…

Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…

Sparse estimation for Gaussian graphical models is a crucial technique for making the relationships among numerous observed variables more interpretable and quantifiable. Various methods have been proposed, including graphical lasso, which…

We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector $X$ has finite mean and covariance. In this setting, the radius of confidence intervals achieved…

Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the…

We consider the problem of simulating a Gaussian vector X, conditional on the fact that each component of X belongs to a finite interval [a_i,b_i], or a semi-finite interval [a_i,+infty). In the one-dimensional case, we design a table-based…

We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an…

The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…