Related papers: On the Coverage Bound Problem of Empirical Likelih…
Discovery problems often require deciding whether additional sampling is needed to detect all categories whose prevalence exceeds a prespecified threshold. We study this question under a Bernoulli product (incidence) model, where categories…
Covering arrays are generalizations of orthogonal arrays that have been widely studied and are used in software testing. The probabilistic method has been employed to derive upper bounds on the sizes of minimum covering arrays and give…
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…
This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…
We address functional uncertainty quantification for ill-posed inverse problems where it is possible to evaluate a possibly rank-deficient forward model, the observation noise distribution is known, and there are known parameter…
We show that two popular selective inference procedures, namely data carving (Fithian et al., 2017) and selection with a randomized response (Tian et al., 2018b), when combined with the polyhedral method (Lee et al., 2016), result in…
We develop a nonparametric extension of the sequential generalized likelihood ratio (GLR) test and corresponding time-uniform confidence sequences for the mean of a univariate distribution. By utilizing a geometric interpretation of the GLR…
We prove new probabilistic upper bounds on generalization error of complex classifiers that are combinations of simple classifiers. Such combinations could be implemented by neural networks or by voting methods of combining the classifiers,…
We prove upper and lower bounds for the threshold of the q-overlap-k-Exact cover problem. These results are motivated by the one-step replica symmetry breaking approach of Statistical Physics, and the hope of using an approach based on that…
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…
Empirical likelihood is an attractive inferential framework that respects natural parameter boundaries, but existing approaches typically require smoothness of the functional and miscalibrate substantially when these assumptions are…
For linear models with spatial errors, the empirical likelihood ratio statistics are constructed for the parameters of the models. It is shown that the limiting distributions of the empirical likelihood ratio statistics are chi-squared…
This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many…
The radiological characterization of contaminated elements (walls, grounds, objects) from nuclear facilities often suffers from a too small number of measurements. In order to determine risk prediction bounds on the level of contamination,…
We study the performance of empirical risk minimization on the $p$-norm linear regression problem for $p \in (1, \infty)$. We show that, in the realizable case, under no moment assumptions, and up to a distribution-dependent constant,…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
This paper presents a method to calculate the exact average block error probability of some random code ensembles under maximum-likelihood decoding. The proposed method is applicable to various channels and ensembles. The focus is on both…
This article discusses the problem of determining whether a given point, or set of points, lies within the convex hull of another set of points in $d$ dimensions. This problem arises naturally in a statistical context when using a…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage to the solutions that fit observations on average, but they do not pay attention to…