Related papers: Efficient Covariance Approximations for Large Spar…
Variational inference offers scalable and flexible tools to tackle intractable Bayesian inference of modern statistical models like Bayesian neural networks and Gaussian processes. For largely over-parameterized models, however, the…
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…
Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…
Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…
Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…
This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and…
We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…
Importance sampling is a promising variance reduction technique for Monte Carlo simulation based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm…
Distributional approximations of (bi--) linear functions of sample variance-covariance matrices play a critical role to analyze vector time series, as they are needed for various purposes, especially to draw inference on the dependence…
Smoothing of noisy sample covariances is an important component in functional data analysis. We propose a novel covariance smoothing method based on penalized splines and associated software. The proposed method is a bivariate spline…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…