Related papers: Tight Lower Bound on the Probability of a Binomial…

Let $P$ be a polynomial of degree $d$ in independent Bernoulli random variables which has zero mean and unit variance. The Bonami hypercontractivity bound implies that the probability that $|P| > t$ decays exponentially in $t^{2/d}$.…

We present a novel analysis of the expected risk of weighted majority vote in multiclass classification. The analysis takes correlation of predictions by ensemble members into account and provides a bound that is amenable to efficient…

Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…

Generalization error bounds are critical to understanding the performance of machine learning models. In this work, building upon a new bound of the expected value of an arbitrary function of the population and empirical risk of a learning…

This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative…

Effective bounds on the union probability are well known to be beneficial in the analysis of stochastic problems in many areas, including probability theory, information theory, statistical communications, computing and operations research.…

The paper presents two results. The first one provides separate conditions for the upper and lower estimate of the distribution of the exit time from balls of a random walk on a weighted graph. The main result of the paper is that the lower…

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…

We present and discuss general techniques for proving inapproximability results for truthful mechanisms. We make use of these techniques to prove lower bounds on the approximability of several non-utilitarian multi-parameter problems. In…

In this paper, we consider the sublinear expectation on bounded random variables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the notion of…

We study a tight Bennett-type concentration inequality for sums of heterogeneous and independent variables, defined as a one-dimensional minimization. We show that this refinement, which outperforms the standard known bounds, remains…

Positive-unlabeled learning (PU learning) is known as a special case of semi-supervised binary classification where only a fraction of positive examples are labeled. The challenge is then to find the correct classifier despite this lack of…

Maximum likelihood estimation is a fundamental computational problem in statistics. In this note, we give a bound for the maximum likelihood degree of algebraic statistical models for discrete data. As usual, such models are identified with…

We consider the problem of sensitivity of threshold risk, defined as the probability of a function of a random variable falling below a specified threshold level $\delta >0.$ We demonstrate that for polynomial and rational functions of that…

The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…

In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…

We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…

Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as…

We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large…

We give a new lower bound for the minimal dispersion of a point set in the unit cube and its inverse function in the high dimension regime. This is done by considering only a very small class of test boxes, which allows us to reduce…