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In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…

High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…

Quadratic discriminant analysis (QDA) is a widely used method for classification problems, particularly preferable over Linear Discriminant Analysis (LDA) for heterogeneous data. However, QDA loses its effectiveness in high-dimensional…

We develop a new randomized iterative algorithm---stochastic dual ascent (SDA)---for finding the projection of a given vector onto the solution space of a linear system. The method is dual in nature: with the dual being a non-strongly…

Though Self-supervised learning (SSL) has been widely studied as a promising technique for representation learning, it doesn't generalize well on long-tailed datasets due to the majority classes dominating the feature space. Recent work…

Real-world training data usually exhibits long-tailed distribution, where several majority classes have a significantly larger number of samples than the remaining minority classes. This imbalance degrades the performance of typical…

High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…

We present a supervised dimensionality reduction technique called Convex Linear Discriminant Analysis (ConvexLDA). The proposed model optimizes a multi-objective cost function by balancing two complementary terms. The first term pulls the…

We consider stochastic convex optimization for heavy-tailed data with the guarantee of being differentially private (DP). Most prior works on differentially private stochastic convex optimization for heavy-tailed data are either restricted…

To jointly tackle the challenges of data and node heterogeneity in decentralized learning, we propose a distributed strong lottery ticket hypothesis (DSLTH), based on which a communication-efficient personalized learning algorithm is…

This work addresses the task of self-supervised learning (SSL) on a long-tailed dataset that aims to learn balanced and well-separated representations for downstream tasks such as image classification. This task is crucial because the real…

Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…

Imbalanced regression occurs when continuous target variables have skewed distributions, creating sparse regions that are difficult for machine learning models to predict accurately. This issue particularly affects neural networks, which…

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…

We analyze the \textit{Large Deviation Probability (LDP)} of linear factor models generated from non-identically distributed components with \textit{regularly-varying} tails, a large subclass of heavy tailed distributions. An efficient…

A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the…

We introduce a novel approach for estimating Latent Dirichlet Allocation (LDA) parameters from collapsed Gibbs samples (CGS), by leveraging the full conditional distributions over the latent variable assignments to efficiently average over…

Domain adaptation (DA) is transfer learning which aims to leverage labeled data in a related source domain to achieve informed knowledge transfer and help the classification of unlabeled data in a target domain. In this paper, we propose a…

The polycystic ovary syndrome diagnosis is a problem that can be leveraged using prognostication based learning procedures. Many implementations of PCOS can be seen with Machine Learning but the algorithms have certain limitations in…

Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…