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We consider training decision trees using noisily labeled data, focusing on loss functions that can lead to robust learning algorithms. Our contributions are threefold. First, we offer novel theoretical insights on the robustness of many…

The purpose of these notes is to provide a systematic quantitative framework - in what is intended to be a "pedagogical" fashion - for discussing mean-reversion and optimization. We start with pair trading and add complexity by following…

In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…

We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…

Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian…

The fundamental task of general density estimation $p(x)$ has been of keen interest to machine learning. In this work, we attempt to systematically characterize methods for density estimation. Broadly speaking, most of the existing methods…

We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…

We examine here what type of predictive modelling, classification, or regression, using neural networks (NN), fits better the task of soft-demapping based post-processing in coherent optical communications, where the transmission channel is…

Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…

Model explainability is crucial for human users to be able to interpret how a proposed classifier assigns labels to data based on its feature values. We study generalized linear models constructed using sets of feature value rules, which…

Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…

We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this…

We study counterfactual regression, which aims to map input features to outcomes under hypothetical scenarios that differ from those observed in the data. This is particularly useful for decision-making when adapting to sudden shifts in…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

Two methods are proposed for high-dimensional shape-constrained regression and classification. These methods reshape pre-trained prediction rules to satisfy shape constraints like monotonicity and convexity. The first method can be applied…

Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…

Ensemble techniques are powerful approaches that combine several weak learners to build a stronger one. As a meta-learning framework, ensemble techniques can easily be applied to many machine learning methods. Inspired by ensemble…

Probabilistic Regression refers to predicting a full probability density function for the target conditional on the features. We present a nonparametric approach to this problem which combines base classifiers (typically gradient boosted…

Finding the hedge ratios for a portfolio and risk compression is the same mathematical problem. Traditionally, regression is used for this purpose. However, regression has its own limitations. For example, in a regression model, we can't…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…