Related papers: 2-coherent and 2-convex Conditional Lower Previsio…

Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…

This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear…

Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…

We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional…

In performative prediction, a predictive model impacts the distribution that generates future data, a phenomenon that is being ignored in classical supervised learning. In this closed-loop setting, the natural measure of performance named…

It is well known that the extension of Watkins' algorithm to general function approximation settings is challenging: does the projected Bellman equation have a solution? If so, is the solution useful in the sense of generating a good…

This paper develops a generalized (quasi-) Bayes framework for conditional moment restriction models, where the parameter of interest is a nonparametric structural function of endogenous variables. We establish contraction rates for a class…

We give a sufficient condition for admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss. Compared to the known results for the multivariate normal case, our…

Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…

Globally optimizing a nonconvex quadratic over the intersection of $m$ balls in $\mathbb{R}^n$ is known to be polynomial-time solvable for fixed $m$. Moreover, when $m=1$, the standard semidefinite relaxation is exact. When $m=2$, it has…

We study the Neyman-Pearson theory for convex expectations (convex risk measures) on $L^{\infty}(\mu)$. Without assuming that the level sets of penalty functions are weakly compact, a new approach different from the convex duality method is…

Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…

Regular vine copulas can describe a wider array of dependency patterns than the multivariate Gaussian copula or the multivariate Student's t copula. This paper presents two contributions related to model selection of regular vine copulas.…

The standard assumption for proving linear convergence of first order methods for smooth convex optimization is the strong convexity of the objective function, an assumption which does not hold for many practical applications. In this…

Chance constraints yield non-convex feasible regions in general. In particular, when the uncertain parameters are modeled by a Wasserstein ball, arXiv:1806.07418 and arXiv:1809.00210 showed that the distributionally robust (pessimistic)…

We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…

This paper establishes various variational properties of parametrized versions of two convexity-preserving constructs that were recently introduced in the literature: the proximal composition of a function and a linear operator, and the…

We introduce cosurfaces with values in the group \(\PC_n(H)\) of \(H\)-valued reciprocal pairwise comparison matrices. The composition law is covariant on upper triangular coefficients and contravariant on lower triangular coefficients,…

Large learning rates, when applied to gradient descent for nonconvex optimization, yield various implicit biases including the edge of stability (Cohen et al., 2021), balancing (Wang et al., 2022), and catapult (Lewkowycz et al., 2020).…

In this research, inferential theory for hypothesis testing under general convex cone alternatives for correlated data is developed. While there exists extensive theory for hypothesis testing under smooth cone alternatives with independent…