Related papers: Sharp Bounds for Mutual Covering

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 derive an (almost) guaranteed upper bound on the error of deep neural networks under distribution shift using unlabeled test data. Prior methods either give bounds that are vacuous in practice or give estimates that are accurate on…

In multi-task learning (MTL) with each task involving graph-dependent data, existing generalization analyses yield a \emph{sub-optimal} risk bound of $O(\frac{1}{\sqrt{n}})$, where $n$ is the number of training samples of each task.…

For Gaussian random fields with values in $\mathbb{R}^d$, sharp upper and lower bounds on the probability of hitting a fixed set have been available for many years. These apply in particular to the solutions of systems of linear SPDEs. For…

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…

Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for…

While machine-learning models are flourishing and transforming many aspects of everyday life, the inability of humans to understand complex models poses difficulties for these models to be fully trusted and embraced. Thus, interpretability…

Given a correlation generated by a (possibly quantum) communication network, we study the amount of shared randomness required to generate it. We develop a novel upper bound for approximating distributions generated by arbitrary networks…

The Lov\'{a}sz Local Lemma (LLL) says that, given a set of bad events that depend on the values of some random variables and where each event happens with probability at most $p$ and depends on at most $d$ other events, there is an…

This paper presents a general methodology for deriving information-theoretic generalization bounds for learning algorithms. The main technical tool is a probabilistic decorrelation lemma based on a change of measure and a relaxation of…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Upper and lower bounds on the error probability of linear codes under maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles of codes on graphs. For upper bounds, focus is put on Gallager bounding techniques and…

This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing independence is very relevant in various applications, distributed independence test is particularly…

A sharp-threshold theorem is proved for box-crossing probabilities on the square lattice. The models in question are the random-cluster model near the self-dual point $p_{\mathrm {sd}}(q)=\sqrt{q}/(1+\sqrt{q})$, the Ising model with…

We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…

We derive novel conditions that guarantee convergence of the Sum-Product algorithm (also known as Loopy Belief Propagation or simply Belief Propagation) to a unique fixed point, irrespective of the initial messages. The computational…

While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several…

This paper establishes the exact strong converse exponent of the soft covering problem in the classical setting. This exponent characterizes the slowest achievable convergence speed of the total variation to one when a code of rate below…

The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…

We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…