Related papers: Distribution-free tests for lossless feature selec…
Understanding the local behaviour of structured multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms, and specifically…
Consider the standard Gaussian linear regression model $Y=X\theta+\epsilon$, where $Y\in R^n$ is a response vector and $ X\in R^{n*p}$ is a design matrix. Numerous work have been devoted to building efficient estimators of $\theta$ when $p$…
Feature screening is an important tool in analyzing ultrahigh-dimensional data, particularly in the field of Omics and oncology studies. However, most attention has been focused on identifying features that have a linear or monotonic impact…
Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
The study of distribution testing has become ubiquitous in the area of property testing, both for its theoretical appeal, as well as for its applications in other fields of Computer Science. The original distribution testing model relies on…
In this letter, we consider multiple statistical classification problem where a sequence of n independent and identically distributed observations, that are generated by one of M discrete sources, need to be classified. The source…
In this paper, we study the challenge of feature selection based on a relatively small collection of sample pairs $\{(x_i, y_i)\}_{1 \leq i \leq m}$. The observations $y_i \in \mathbb{R}$ are thereby supposed to follow a noisy single-index…
We consider the problem of learning linear classifiers when both features and labels are binary. In addition, the features are noisy, i.e., they could be flipped with an unknown probability. In Sy-De attribute noise model, where all…
Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…
Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…
This paper presents a principled approach for detecting out-of-distribution (OOD) samples in deep neural networks (DNN). Modeling probability distributions on deep features has recently emerged as an effective, yet computationally cheap…
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…
We study the problem of testing whether a function $f: \mathbb{R}^n \to \mathbb{R}$ is a polynomial of degree at most $d$ in the \emph{distribution-free} testing model. Here, the distance between functions is measured with respect to an…
In this study, we propose a method Distributionally Robust Safe Screening (DRSS), for identifying unnecessary samples and features within a DR covariate shift setting. This method effectively combines DR learning, a paradigm aimed at…
Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…
This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for…
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…
We consider the following basic inference problem: there is an unknown high-dimensional vector $w \in \mathbb{R}^n$, and an algorithm is given access to labeled pairs $(x,y)$ where $x \in \mathbb{R}^n$ is a measurement and $y = w \cdot x +…
The uncertainty quantification and error control of classifiers are crucial in many high-consequence decision-making scenarios. We propose a selective classification framework that provides an indecision option for any observations that…