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Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright…

The increasing complexity of data requires methods and models that can effectively handle intricate structures, as simplifying them would result in loss of information. While several analytical tools have been developed to work with complex…

Regression with the lasso penalty is a popular tool for performing dimension reduction when the number of covariates is large. In many applications of the lasso, like in genomics, covariates are subject to measurement error. We study the…

We consider the problem of regression learning for deterministic design and independent random errors. We start by proving a sharp PAC-Bayesian type bound for the exponentially weighted aggregate (EWA) under the expected squared empirical…

Threshold Autoregressive (TAR) models have been widely used by statisticians for non-linear time series forecasting during the past few decades, due to their simplicity and mathematical properties. On the other hand, in the forecasting…

Confounding is a significant obstacle to unbiased estimation of causal effects from observational data. For settings with high-dimensional covariates -- such as text data, genomics, or the behavioral social sciences -- researchers have…

Predictive models make mistakes. Hence, there is a need to quantify the uncertainty associated with their predictions. Conformal inference has emerged as a powerful tool to create statistically valid prediction regions around point…

High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a…

We develop a theoretical framework for the analysis of oblique decision trees, where the splits at each decision node occur at linear combinations of the covariates (as opposed to conventional tree constructions that force axis-aligned…

It has been known for a long time that stratification is one possible strategy to obtain higher convergence rates for the Monte Carlo estimation of integrals over the hyper-cube $[0, 1]^s$ of dimension $s$. However, stratified estimators…

Machine learning problems with multiple objective functions appear either in learning with multiple criteria where learning has to make a trade-off between multiple performance metrics such as fairness, safety and accuracy; or, in…

In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be…

In human microbiome studies, sequencing reads data are often summarized as counts of bacterial taxa at various taxonomic levels specified by a taxonomic tree. This paper considers the problem of analyzing two repeated measurements of…

We consider the problem of computationally-efficient prediction from high dimensional and highly correlated predictors in challenging settings where accurate variable selection is effectively impossible. Direct application of penalization…

Ensemble methods are among the state-of-the-art predictive modeling approaches. Applied to modern big data, these methods often require a large number of sub-learners, where the complexity of each learner typically grows with the size of…

Accurately estimating personalized treatment effects within a study site (e.g., a hospital) has been challenging due to limited sample size. Furthermore, privacy considerations and lack of resources prevent a site from leveraging…

This paper presents a novel nonlinear regression model for estimating heterogeneous treatment effects from observational data, geared specifically towards situations with small effect sizes, heterogeneous effects, and strong confounding.…

We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…

This paper studies covariate adjusted estimation of the average treatment effect in stratified experiments. We work in a general framework that includes matched tuples designs, coarse stratification, and complete randomization as special…

We consider the analysis of high dimensional data given in the form of a matrix with columns consisting of observations and rows consisting of features. Often the data is such that the observations do not reside on a regular grid, and the…