Related papers: Multiscale Fisher's Independence Test for Multivar…
This paper develops an inferential theory for high-dimensional matrix-variate factor models with missing observations. We propose an easy-to-use all-purpose method that involves two straightforward steps. First, we perform principal…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
It is well known that non-parametric methods suffer from the "curse of dimensionality". We propose here a new estimation method for a multivariate distribution, using sub-sampling and ranks, which seems not to suffer from this "curse". We…
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…
We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach, which we call MINT, is based on the estimation of mutual information, whose decomposition into joint and…
In this paper, we introduce a ${\mathcal L}_2$ type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed based on the pairwise distance covariance and it accounts for the…
We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…
Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between…
We present and evaluate the Fast (conditional) Independence Test (FIT) -- a nonparametric conditional independence test. The test is based on the idea that when $P(X \mid Y, Z) = P(X \mid Y)$, $Z$ is not useful as a feature to predict $X$,…
We study the problem of independence and conditional independence tests between categorical covariates and a continuous response variable, which has an immediate application in genetics. Instead of estimating the conditional distribution of…
Linear mixed models are widely used to analyze non-independent data, but inference for fixed effects can be unreliable under misspecification of the random-effects distribution, inaccurate Fisher information estimation, or convergence…
Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any…
We introduce a new methodology for analyzing serial data by quantile regression assuming that the underlying quantile function consists of constant segments. The procedure does not rely on any distributional assumption besides serial…
Fisher's exact test is often a preferred method to estimate the significance of statistical dependence. However, in large data sets the test is usually too worksome to be applied, especially in an exhaustive search (data mining). The…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
High dimensional space-time data pose known computational challenges when fitting spatio-temporal models. Such data show dependence across several dimensions of space as well as in time, and can easily involve hundreds of thousands of…
Distributions over rankings are used to model data in a multitude of real world settings such as preference analysis and political elections. Modeling such distributions presents several computational challenges, however, due to the…
A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties of the copulas are proved. They allow us…
We describe a novel non-parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables us to determine whether one source variable is significantly more…
The aim of this thesis is to find a solution to the non-parametric independence problem in separable metric spaces. Suppose we are given finite collection of samples from an i.i.d. sequence of paired random elements, where each marginal has…