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Calibration is a frequently invoked concept when useful label probability estimates are required on top of classification accuracy. A calibrated model is a function whose values correctly reflect underlying label probabilities. Calibration…

Multi-step forecasting is often described through a simple rule of thumb: recursive strategies are said to have high bias and low variance, while direct strategies are said to have low bias and high variance. We revisit this belief by…

Classification is a major tool of statistics and machine learning. A classification method first processes a training set of objects with given classes (labels), with the goal of afterward assigning new objects to one of these classes. When…

The incorporation of unlabeled data in regression and classification analysis is an increasing focus of the applied statistics and machine learning literatures, with a number of recent examples demonstrating the potential for unlabeled data…

Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…

We present a new model for prediction markets, in which we use risk measures to model agents and introduce a market maker to describe the trading process. This specific choice on modelling tools brings us mathematical convenience. The…

This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…

The varying-coefficient model is a strong tool for the modelling of interactions in generalized regression. It is easy to apply if both the variables that are modified as well as the effect modifiers are known. However, in general one has a…

Forecasting with longitudinal data has been rarely studied. Most of the available studies are for continuous response and all of them are for univariate response. In this study, we consider forecasting multivariate longitudinal binary data.…

Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter…

We investigate graph representation learning approaches that enable models to generalize across graphs: given a model trained using the representations from one graph, our goal is to apply inference using those same model parameters when…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

Accurately predicting future behaviors of surrounding vehicles is an essential capability for autonomous vehicles in order to plan safe and feasible trajectories. The behaviors of others, however, are full of uncertainties. Both rational…

Scatter plots carry an implicit if subtle message about causality. Whether we look at functions of one variable in pure mathematics, plots of experimental measurements as a function of the experimental conditions, or scatter plots of…

Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…

In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional)…

We consider problems where multiple predictions can be considered correct, but only one of them is given as supervision. This setting differs from both the regression and class-conditional generative modelling settings: in the former, there…

Graph Machine Learning (GML) has numerous applications, such as node/graph classification and link prediction, in real-world domains. Providing human-understandable explanations for GML models is a challenging yet fundamental task to foster…

We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Often this data is transposable, meaning that both the row variables and column variables are of potential interest. An example…