Related papers: A $U$-classifier for high-dimensional data under n…

Classification is an important task in many fields including biomedical research and machine learning. Traditionally, a classification rule is constructed based a bunch of labeled data. Recently, due to technological innovation and…

We define cyclic $U$-statistics as a variant of $U$-statistics based on variables $X_1,\dots,X_n$ that are assumed to be cyclically ordered. We also define alternating $U$-statistics where in the definition terms are summed with alternating…

High-dimensional linear classifiers, such as the support vector machine (SVM) and distance weighted discrimination (DWD), are commonly used in biomedical research to distinguish groups of subjects based on a large number of features.…

A random sampling function Sample:U->{0,1} for a key universe U is a distinguisher with probability p if for any given assignment of values v(x) to the keys x in U, including at least one non-zero v(x)!=0, the sampled sum sum{ v(x) | x in U…

We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…

The one-class classification problem is a well-known research endeavor in pattern recognition. The problem is also known under different names, such as outlier and novelty/anomaly detection. The core of the problem consists in modeling and…

Conventional statistical wisdom established a well-understood relationship between model complexity and prediction error, typically presented as a U-shaped curve reflecting a transition between under- and overfitting regimes. However,…

Feature selection is frequently used as a pre-processing step to machine learning. It is a process of choosing a subset of original features so that the feature space is optimally reduced according to a certain evaluation criterion. The…

We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of…

The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly…

The linear classifier is widely used in various image classification tasks. It works by optimizing the distance between a sample and its corresponding class center. However, in real-world data, one class can contain several local clusters,…

Universal domain adaptation (UniDA) is a general unsupervised domain adaptation setting, which addresses both domain and label shifts in adaptation. Its main challenge lies in how to identify target samples in unshared or unknown classes.…

This paper studies the principal components (PC) estimator for high dimensional approximate factor models with weak factors in that the factor loading ($\boldsymbol{\Lambda}^0$) scales sublinearly in the number $N$ of cross-section units,…

This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned…

Three important issues are often encountered in Supervised and Semi-Supervised Classification: class-memberships are unreliable for some training units (label noise), a proportion of observations might depart from the main structure of the…

We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…

Huge amount of applications in various fields, such as gene expression analysis or computer vision, undergo data sets with high-dimensional low-sample-size (HDLSS), which has putted forward great challenges for standard statistical and…

This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…

In this paper, we investigate hypothesis testing for the linear combination of mean vectors across multiple populations through the method of random integration. We have established the asymptotic distributions of the test statistics under…

This paper introduces a generic method which enables to use conventional deep neural networks as end-to-end one-class classifiers. The method is based on splitting given data from one class into two subsets. In one-class classification,…