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Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…

Data-driven algorithms are only as good as the data they work with, while data sets, especially social data, often fail to represent minorities adequately. Representation Bias in data can happen due to various reasons ranging from…

Branching and weak probabilistic bisimilarities are two well-known notions capturing behavioral equivalence between nondeterministic probabilistic systems. For probabilistic systems, divergence is of major concern. Recently several…

We introduce a new cost function over experiments, f-information, based on the theory of multivariate statistical divergences, that generalizes Sims's classic model of rational inattention as well as the class of posterior-separable cost…

Intersectionality is a framework that analyzes how interlocking systems of power and oppression affect individuals along overlapping dimensions including race, gender, sexual orientation, class, and disability. Intersectionality theory…

We introduce a methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or {\gamma}-divergence), indexed by a single tuning parameter. It is well known that the posterior density induced by robust…

This paper considers the two-dataset problem, where data are collected from two potentially different populations sharing common aspects. This problem arises when data are collected by two different types of researchers or from two…

Ideally, any statistical inference should be robust to local influences. Although there are simple ways to check about leverage points in independent and linear problems, more complex models require more sophisticated methods.…

Feynman integrals can be expanded asymptotically with respect to some small parameters at the integrand level, a technique known as the expansion by regions. A naive expansion by regions may break down due to divergences not regulated by…

What can be more fascinating than {\it experimental metaphysics}, to quote one of Abner Shimony's enlightening expressions? Bell inequalities are at the heart of the study of nonlocality. I present a list of open questions, organised in…

The paper analyses the convergence of the $p$-version of the FEM when the solution is piecewise analytic function. It focuses on pointwise convergence of the gradient. It shows that at boundary the rate is different than inside the element…

The foremost challenge to causal inference with real-world data is to handle the imbalance in the covariates with respect to different treatment options, caused by treatment selection bias. To address this issue, recent literature has…

In practice, and especially when training deep neural networks, visual recognition rules are often learned based on various sources of information. On the other hand, the recent deployment of facial recognition systems with uneven…

This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the…

The bias-variance decomposition is a central result in statistics and machine learning, but is typically presented only for the squared error. We present a generalization of the bias-variance decomposition where the prediction error is a…

Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a…

The counterfactual distribution models the effect of the treatment in the untreated group. While most of the work focuses on the expected values of the treatment effect, one may be interested in the whole counterfactual distribution or…

A key recent advance in face recognition models a test face image as a sparse linear combination of a set of training face images. The resulting sparse representations have been shown to possess robustness against a variety of distortions…

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…

This paper analyzes irrelevance and independence relations in graphical models associated with convex sets of probability distributions (called Quasi-Bayesian networks). The basic question in Quasi-Bayesian networks is, How can…