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Missing data theory deals with the statistical methods in the occurrence of missing data. Missing data occurs when some values are not stored or observed for variables of interest. However, most of the statistical theory assumes that data…

Causal inference is central to many areas of artificial intelligence, including complex reasoning, planning, knowledge-base construction, robotics, explanation, and fairness. An active community of researchers develops and enhances…

Much of scientific data is collected as randomized experiments intervening on some and observing other variables of interest. Quite often, a given phenomenon is investigated in several studies, and different sets of variables are involved…

Instrumental variables have proven useful, in particular within the social sciences and economics, for making inference about the causal effect of a random variable, B, on another random variable, C, in the presence of unobserved…

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…

We consider basic conceptual questions concerning the relationship between statistical estimation and causal inference. Firstly, we show how to translate causal inference problems into an abstract statistical formalism without requiring any…

Conditionally specified models are often used to describe complex multivariate data. Such models assume implicit structures on the extremes. So far, no methodology exists for calculating extremal characteristics of conditional models since…

Semi-supervised learning has attracted significant attention due to the proliferation of applications featuring limited labeled data but abundant unlabeled data. In this paper, we examine the statistical inference problem in an…

Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

Partial-label learning is a kind of weakly-supervised learning with inexact labels, where for each training example, we are given a set of candidate labels instead of only one true label. Recently, various approaches on partial-label…

Generalized latent factor analysis not only provides a useful latent embedding approach in statistics and machine learning, but also serves as a widely used tool across various scientific fields, such as psychometrics, econometrics, and…

In this paper, we explore bounds on the expected risk when using deep neural networks for supervised classification from an information theoretic perspective. Firstly, we introduce model risk and fitting error, which are derived from…

Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…

Probing experiments investigate the extent to which neural representations make properties -- like part-of-speech -- predictable. One suggests that a representation encodes a property if probing that representation produces higher accuracy…

Measurement error can often be harmful when estimating causal effects. Two scenarios in which this is the case are in the estimation of (a) the average treatment effect when confounders are measured with error and (b) the natural indirect…

A crucial input into causal inference is the imputed counterfactual outcome. Imputation error can arise because of sampling uncertainty from estimating the prediction model using the untreated observations, or from out-of-sample information…

This paper provides partial identification of various binary choice models with misreported dependent variables. We propose two distinct approaches by exploiting different instrumental variables respectively. In the first approach, the…

This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…