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There is currently a large gap in performance between the statistically rigorous methods like linear regression or additive splines and the powerful deep methods using neural networks. Previous works attempting to close this gap have failed…

This paper is concerned with the problems of interaction screening and nonlinear classification in a high-dimensional setting. We propose a two-step procedure, IIS-SQDA, where in the first step an innovated interaction screening (IIS)…

Gini distance correlation (GDC) was recently proposed to measure the dependence between a categorical variable, Y, and a numerical random vector, X. It mutually characterizes independence between X and Y. In this article, we utilize the GDC…

Microarray studies, in order to identify genes associated with an outcome of interest, usually produce noisy measurements for a large number of gene expression features from a small number of subjects. One common approach to analyzing such…

Many problems require the selection of a subset of variables from a full set of optimization variables. The computational complexity of an exhaustive search over all possible subsets of variables is, however, prohibitively expensive,…

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…

Feature or variable selection is a problem inherent to large data sets. While many methods have been proposed to deal with this problem, some can scale poorly with the number of predictors in a data set. Screening methods scale linearly…

Many processes of scientific and technological interest are characterized by time scales that render their simulation impossible if one uses present day simulation capabilities. To overcome this challenge a variety of enhanced simulation…

Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…

We propose the conditional predictive impact (CPI), a consistent and unbiased estimator of the association between one or several features and a given outcome, conditional on a reduced feature set. Building on the knockoff framework of…

Disentangled representation learning aims to uncover latent variables underlying the observed data, and generally speaking, rather strong assumptions are needed to ensure identifiability. Some approaches rely on sufficient changes on the…

In high dimensional analysis, effects of explanatory variables on responses sometimes rely on certain exposure variables, such as time or environmental factors. In this paper, to characterize the importance of each predictor, we utilize its…

This paper deals with the maximum independent set (M.I.S.) problem, also known as the stable set problem. The basic mathematical programming model that captures this problem is an Integer Program (I.P.) with zero-one variables $x_j$ and…

Abstract Visual Reasoning (AVR) comprises a wide selection of various problems similar to those used in human IQ tests. Recent years have brought dynamic progress in solving particular AVR tasks, however, in the contemporary literature AVR…

When observations are independent, formulae and software are readily available to plan and design studies of appropriate size and power to detect important associations. When observations are correlated or clustered, results obtained from…

This paper studies the distributed conditional feature screening for massive data with ultrahigh-dimensional features. Specifically, three distributed partial correlation feature screening methods (SAPS, ACPS and JDPS methods) are firstly…

Feature selection is popular for obtaining small, interpretable, yet highly accurate prediction models. Conventional feature-selection methods typically yield one feature set only, which might not suffice in some scenarios. For example,…

In this paper we present a method to generate independent samples for a general random variable, either continuous or discrete. The algorithm is an extension of the acceptance-rejection method, and it is particularly useful for kinetic…

The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…

We consider the problem of model-based clustering in the presence of many correlated, mixed continuous and discrete variables, some of which may have missing values. Discrete variables are treated with a latent continuous variable approach…