Related papers: A Global Homogeneity Test for High-Dimensional Lin…

Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…

Microarray is a technology to quantitatively monitor the expression of large number of genes in parallel. It has become one of the main tools for global gene expression analysis in molecular biology research in recent years. The large…

The problem of inferring unknown graph edges from numerical data at a graph's nodes appears in many forms across machine learning. We study a version of this problem that arises in the field of \emph{landscape genetics}, where genetic…

Multi-trait genome-wide association studies (GWAS) use multi-variate statistical methods to identify associations between genetic variants and multiple correlated traits simultaneously, and have higher statistical power than independent…

Comparing large covariance matrices has important applications in modern genomics, where scientists are often interested in understanding whether relationships (e.g., dependencies or co-regulations) among a large number of genes vary…

The problem of identifying change points in high-dimensional Gaussian graphical models (GGMs) in an online fashion is of interest, due to new applications in biology, economics and social sciences. The offline version of the problem, where…

Genetical genomics experiments have now been routinely conducted to measure both the genetic markers and gene expression data on the same subjects. The gene expression levels are often treated as quantitative traits and are subject to…

One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…

Motivation: Networks underlie the generation and interpretation of many biological datasets: gene networks shed light on the regulatory structure of the genome, and cell networks can capture structure of the tumor micro-environment.…

This paper studies generative adversarial networks (GANs) from the perspective of statistical inference. A GAN is a popular machine learning method in which the parameters of two neural networks, a generator and a discriminator, are…

We generalize Levene's test for variance (scale) heterogeneity between $k$ groups for more complex data, which includes sample correlation and group membership uncertainty. Following a two-stage regression framework, we show that least…

We consider a method to jointly estimate sparse precision matrices and their underlying graph structures using dependent high-dimensional datasets. We present a penalized maximum likelihood estimator which encourages both sparsity and…

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology…

We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

In this article, we study the problem of high-dimensional conditional independence testing, a key building block in statistics and machine learning. We propose an inferential procedure based on double generative adversarial networks (GANs).…

We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…

For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…

We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the…