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The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

The coefficient of determination is well defined for linear models and its extension is long wanted for mixed-effects models. We revisit its extension to define measures for proportions of variation explained by the whole model, fixed…

A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify this assumption from a single dataset. Under the assumption of independent causal mechanisms…

Causal models with unobserved variables impose nontrivial constraints on the distributions over the observed variables. When a common cause of two variables is unobserved, it is impossible to uncover the causal relation between them without…

The literature has covered the features and uses of the traditional univariate and bivariate logistic distributions in great detail. It is reasonable to wonder, though, if logistic marginals and conditionals could exhibit a similar…

Linear regression is a frequently used tool in statistics, however, its validity and interpretability relies on strong model assumptions. While robust estimates of the coefficients' covariance extend the validity of hypothesis tests and…

Predictive inference under a general regression setting is gaining more interest in the big-data era. In terms of going beyond point prediction to develop prediction intervals, two main threads of development are conformal prediction and…

An important phenomenon in high dimensional biological data is the presence of unobserved covariates that can have a significant impact on the measured response. When these factors are also correlated with the covariate(s) of interest (i.e.…

Generative models are increasingly deployed as substitutes for real data in downstream scientific workflows, yet standard evaluation criteria remain focused on marginal distribution matching. We argue that this represents a fundamental gap:…

It has been argued that in supervised classification tasks, in practice it may be more sensible to perform model selection with respect to some more focused model selection score, like the supervised (conditional) marginal likelihood, than…

We consider the problem of predicting a response $Y$ from a set of covariates $X$ when test and training distributions differ. Since such differences may have causal explanations, we consider test distributions that emerge from…

Conditional Kendall's tau is a measure of dependence between two random variables, conditionally on some covariates. We assume a regression-type relationship between conditional Kendall's tau and some covariates, in a parametric setting…

As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…

Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate…

We investigate generically applicable and intuitively appealing prediction intervals based on $k$-fold cross validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training…

This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…

There has been a lot of work fitting Ising models to multivariate binary data in order to understand the conditional dependency relationships between the variables. However, additional covariates are frequently recorded together with the…

Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…

For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…

Inferential models have been proposed for valid and efficient prior-free probabilistic inference. As it gradually gained popularity, this theory is subject to further developments for practically challenging problems. This paper considers…