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Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the…

We introduce varbvs, a suite of functions written in R and MATLAB for regression analysis of large-scale data sets using Bayesian variable selection methods. We have developed numerical optimization algorithms based on variational…

There is emerging interest in performing regression between distributions. In contrast to prediction on single instances, these machine learning methods can be useful for population-based studies or on problems that are inherently…

General circulation models (GCMs) are essential tools for climate studies. Such climate models may have varying accuracy across the input domain, but no model is uniformly best. One can improve climate model prediction performance by…

Reliability-based optimization (RBO) is crucial for identifying optimal risk-informed decisions for designing and operating engineering systems. However, its computation remains challenging as it requires a concurrent task of optimization…

We propose a new ensemble prediction method, Random Subset Averaging (RSA), tailored for settings with many covariates, particularly in the presence of strong correlations. RSA constructs candidate models via binomial random subset strategy…

Finite-sample bias is a pervasive challenge in the estimation of structural equation models (SEMs), especially when sample sizes are small or measurement reliability is low. A range of methods have been proposed to improve finite-sample…

We study fast algorithms for statistical regression problems under the strong contamination model, where the goal is to approximately optimize a generalized linear model (GLM) given adversarially corrupted samples. Prior works in this line…

Evidence theory is widely used in decision-making and reasoning systems. In previous research, Transferable Belief Model (TBM) is a commonly used evidential decision making model, but TBM is a non-preference model. In order to better fit…

We herein propose a new robust estimation method based on random projections that is adaptive and, automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted…

Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is…

The standard model of online prediction deals with serial processing of inputs by a single processor. However, in large-scale online prediction problems, where inputs arrive at a high rate, an increasingly common necessity is to distribute…

We propose a fast and efficient strategy, called the representative approach, for big data analysis with generalized linear models, especially for distributed data with localization requirements or limited network bandwidth. With a given…

Machine learning models for continuous outcomes often yield systematically biased predictions, particularly for values that largely deviate from the mean. Specifically, predictions for large-valued outcomes tend to be negatively biased…

In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…

Ridge regression is a well established regression estimator which can conveniently be adapted for classification problems. One compelling reason is probably the fact that ridge regression emits a closed-form solution thereby facilitating…

Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…

The primary goal of my Ph.D. study is to develop provably efficient and practical algorithms for data-driven sequential decision-making under uncertainty. My work focuses on reinforcement learning (RL), multi-armed bandits, and their…

The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…