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We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in…

Theories can be represented as statistical models for empirical testing. There is a vast literature on model selection and multimodel inference that focuses on how to assess which statistical model, and therefore which theory, best fits the…

This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…

In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…

When considering a model architecture, there are several ways to reduce its memory footprint. Historically, popular approaches included selecting smaller architectures and creating sparse networks through pruning. More recently, randomized…

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional…

Variable importance (VI) methods are often used for hypothesis generation, feature selection, and scientific validation. In the standard VI pipeline, an analyst estimates VI for a single predictive model with only the observed features.…

Different prediction models might perform equally well (Rashomon set) in the same task, but offer conflicting interpretations and conclusions about the data. The Rashomon effect in the context of Explainable AI (XAI) has been recognized as…

Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of…

Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…

Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability…

A basic model in sequential decision making is the Markov decision process (MDP), which is extended to Robust MDPs (RMDPs) by allowing uncertainty in transition probabilities and optimizing against the worst-case transition probabilities…

This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…

This paper explores the homogeneity of coefficients in high-dimensional regression, which extends the sparsity concept and is more general and suitable for many applications. Homogeneity arises when one expects regression coefficients…

Combining machine learning with econometric analysis is becoming increasingly prevalent in both research and practice. A common empirical strategy involves the application of predictive modeling techniques to 'mine' variables of interest…

This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…

We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and…

Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…

A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…