Related papers: On Non-Interactive Simulation of Binary Random Var…
We show an essentially tight bound on the number of adaptively chosen statistical queries that a computationally efficient algorithm can answer accurately given $n$ samples from an unknown distribution. A statistical query asks for the…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
This article is a survey of results concerning an inequality, which may be seen as a versatile tool to solve problems in the domain of Applied Probability. The inequality, which we call BRS-inequality, gives a convenient upper bound for the…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
In this paper we derive new upper bounds for the densities of measurable sets in R^n which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new…
Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
We study channel simulation under common randomness assistance in the finite-blocklength regime and identify the smooth channel max-information as a linear program one-shot converse on the minimal simulation cost for fixed error tolerance.…
We consider the binary classification problem when data are large and subject to unknown but bounded uncertainties. We address the problem by formulating the nonlinear support vector machine training problem with robust optimization. To do…
Increasingly demanding performance requirements for dynamical systems motivates the adoption of nonlinear and adaptive control techniques. One challenge is the nonlinearity of the resulting closed-loop system complicates verification that…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…
We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study…
Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and…
Estimating and optimizing Mutual Information (MI) is core to many problems in machine learning; however, bounding MI in high dimensions is challenging. To establish tractable and scalable objectives, recent work has turned to variational…
Cut-set bounds on achievable rates for network communication protocols are not in general tight. In this paper we introduce a new technique for proving converses for the problem of transmission of correlated sources in networks, that…
Delsarte's method and its extensions allow to consider the upper bound problem for codes in 2-point-homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that…
All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…
Finite blocklength and second-order (dispersion) results are presented for the arbitrarily-varying channel (AVC), a classical model wherein an adversary can transmit arbitrary signals into the channel. A novel finite blocklength…