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In finite volume the partition function of QCD with a given $\theta$ is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed…
Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this…
Rating systems are ubiquitous, with applications ranging from product recommendation to teaching evaluations. Confidence intervals for functionals of rating data such as empirical means or quantiles are critical to decision-making in…
Testing intersections of null-hypotheses is an integral part of closed testing procedures for assessing multiple null-hypotheses under family-wise type 1 error control. Popular intersection tests such as the minimum p-value test are based…
This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The…
Convergence bounds are one of the main tools to obtain information on the performance of a distributed machine learning task, before running the task itself. In this work, we perform a set of experiments to assess to which extent, and in…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
An influential line of recent work has focused on the generalization properties of unregularized gradient-based learning procedures applied to separable linear classification with exponentially-tailed loss functions. The ability of such…
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…
The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space,…
We consider the functional given by the product of the first Dirichlet eigenvalue and the torsional rigidity of planar domains normalized by the area. This scale invariant functional was studied by P\'olya and Szeg\H{o} in 1951 who showed…
Rational functions of total degree $l$ in n variables have a representation in the Bernstein form defined over $n$ dimensional simplex. The range of a rational function is bounded by the smallest and the largest rational Bernstein…
The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function…
The paper is devoted to tests for uniformity based on sum-functions of overlapping spacings, where the order of spacings can diverge to infinity as the sample size increases. In particular, it is shown that the asymptotic local power of…
An optimal control problem on finite-dimensional positive cones is stated. Under a critical assumption on the cone, the corresponding Bellman equation is satisfied by a linear function, which can be computed by convex optimization. A…
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…
Quantifying uncertainty using confidence regions is a central goal of statistical inference. Despite this, methodologies for confidence bands in Functional Data Analysis are still underdeveloped compared to estimation and hypothesis…
This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…
We improve both upper and lower bounds for the distribution-free testing of monotone conjunctions. Given oracle access to an unknown Boolean function $f:\{0,1\}^n \rightarrow \{0,1\}$ and sampling oracle access to an unknown distribution…
Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the…