Related papers: Distribution-free tests for lossless feature selec…
We study the excess minimum risk in statistical inference, defined as the difference between the minimum expected loss in estimating a random variable from an observed feature vector and the minimum expected loss in estimating the same…
In this paper, we investigate the problem of classifying feature vectors with mutually independent but non-identically distributed elements. First, we show the importance of this problem. Next, we propose a classifier and derive an…
We derive a new asymptotic expansion for the global excess risk of a local-$k$-nearest neighbour classifier, where the choice of $k$ may depend upon the test point. This expansion elucidates conditions under which the dominant contribution…
`Distribution regression' refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y=f(P) + mu where f is an unknown regression function and mu is a random error. Typically, we…
We study the problem nonparametric classification with repeated observations. Let $\bX$ be the $d$ dimensional feature vector and let $Y$ denote the label taking values in $\{1,\dots ,M\}$. In contrast to usual setup with large sample size…
Let $(Y,X_1,...,X_m)$ be a random vector. It is desired to predict $Y$ based on $(X_1,...,X_m)$. Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the…
Feature selection problems have been extensively studied for linear estimation, for instance, Lasso, but less emphasis has been placed on feature selection for non-linear functions. In this study, we propose a method for feature selection…
We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with $k$ $>>$ $n$ regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension…
We provide efficient algorithms for the problem of distribution learning from high-dimensional Gaussian data where in each sample, some of the variable values are missing. We suppose that the variables are missing not at random (MNAR). The…
High-dimensional linear regression has been thoroughly studied in the context of independent and identically distributed data. We propose to investigate high-dimensional regression models for independent but non-identically distributed…
We consider the problem of estimating a $d$-dimensional $s$-sparse discrete distribution from its samples observed under a $b$-bit communication constraint. The best-known previous result on $\ell_2$ estimation error for this problem is…
High-dimensional feature selection is a central problem in a variety of application domains such as machine learning, image analysis, and genomics. In this paper, we propose graph-based tests as a useful basis for feature selection. We…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…
We propose a novel statistical test to assess the mutual independence of multidimensional random vectors. Our approach is based on the $L_1$-distance between the joint density function and the product of the marginal densities associated…
This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…
This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…
This paper studies model checking for general parametric regression models having no dimension reduction structures on the predictor vector. Using any U-statistic type test as an initial test, this paper combines the sample-splitting and…
The task of the binary classification problem is to determine which of two distributions has generated a length-$n$ test sequence. The two distributions are unknown; two training sequences of length $N$, one from each distribution, are…
The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. The least absolute shrinkage and selection operator (Lasso) allows computationally efficient feature selection…