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Researchers are often interested in understanding the relationship between a set of covariates and a set of response variables. To achieve this goal, the use of regression analysis, either linear or generalized linear models, is largely…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory…
Probabilistic models inform an increasingly broad range of business and policy decisions ultimately made by people. Recent algorithmic, computational, and software framework development progress facilitate the proliferation of Bayesian…
High-dimensional multivariate longitudinal data, which arise when many outcome variables are measured repeatedly over time, are becoming increasingly common in social, behavioral and health sciences. We propose a latent variable model for…
Extensions of previous linear regression models for interval data are presented. A more flexible simple linear model is formalized. The new model may express cross-relationships between mid-points and spreads of the interval data in a…
The wide-spread adoption of representation learning technologies in clinical decision making strongly emphasizes the need for characterizing model reliability and enabling rigorous introspection of model behavior. While the former need is…
Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…
Prediction-powered inference is a framework for performing valid statistical inference when an experimental dataset is supplemented with predictions from a machine-learning system. The framework yields simple algorithms for computing…
Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…
Predictions about people, such as their expected educational achievement or their credit risk, can be performative and shape the outcome that they aim to predict. Understanding the causal effect of these predictions on the eventual outcomes…
The ubiquity of machine learning based predictive models in modern society naturally leads people to ask how trustworthy those models are? In predictive modeling, it is quite common to induce a trade-off between accuracy and…
Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…
We propose a new modeling approach that is a generalization of generative and discriminative models. The core idea is to use an implicit parameterization of a joint probability distribution by specifying only the conditional distributions.…
In some real world situations, linear models are not sufficient to represent accurately complex relations between input variables and output variables of a studied system. Multilayer Perceptrons are one of the most successful non-linear…
We present a comprehensive study of graphical log-linear models for contingency tables. High dimensional contingency tables arise in many areas such as computational biology, collection of survey and census data and others. Analysis of…
The main objective of explanations is to transmit knowledge to humans. This work proposes to construct informative explanations for predictions made from machine learning models. Motivated by the observations from social sciences, our…
This paper presents a significant advancement in the estimation of the Composite Link Model within a penalized likelihood framework, specifically designed to address indirect observations of grouped count data. While the model is effective…
Probability forecasting is common in the geosciences, the finance sector, and elsewhere. It is sometimes the case that one has multiple probability-forecasts for the same target. How is the information in these multiple forecast systems…
An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…