Related papers: Intractability results for integration in tensor p…
We present a lower error bound for approximating linear multivariate operators defined over Hilbert spaces in terms of the error bounds for appropriately constructed linear functionals as long as algorithms use function values. Furthermore,…
In this work we consider the problem of numerical integration, i.e., approximating integrals with respect to a target probability measure using only pointwise evaluations of the integrand. We focus on the setting in which the target…
We establish new lower-bounds for the information complexity of mixed-integer convex optimization under two "bit-wise" oracles. The first oracle provides bits of first-order information in the standard coordinate model, and the second…
Numerical integration over the real line for analytic functions is studied. Our main focus is on the sharpness of the error bounds. We first derive two general lower estimates for the worst-case integration error, and then apply these to…
We describe a convex programming approach to the calculation of lower bounds on the minimum cost of constrained decentralized control problems with nonclassical information structures. The class of problems we consider entail the…
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…
Unlike matrix completion, tensor completion does not have an algorithm that is known to achieve the information-theoretic sample complexity rate. This paper develops a new algorithm for the special case of completion for nonnegative…
Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic…
We study multivariate integration of functions that are invariant under permutations (of subsets) of their arguments. We find an upper bound for the $n$th minimal worst case error and show that under certain conditions, it can be bounded…
This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…
It is folklore particularly in numerical and computer sciences that, instead of solving some general problem f:A->B, additional structural information about the input x in A (that is any kind of promise that x belongs to a certain subset A'…
In this paper we introduce a reproducing kernel Hilbert space defined on $\mathbb{R}^{d+1}$ as the tensor product of a reproducing kernel defined on the unit sphere $\mathbb{S}^{d}$ in $\mathbb{R}^{d+1}$ and a reproducing kernel defined on…
Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to…
We study distributed inner product estimation for $n$-qubit states using local randomized measurements, for which rigorous worst-case guarantees are less understood. We first reduce the minimax kernel optimization to Hamming-distance…
The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in…
For objects belonging to a known model set and observed through a prescribed linear process, we aim at determining methods to recover linear quantities of these objects that are optimal from a worst-case perspective. Working in a Hilbert…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
In this dissertation we study the tractability of the information-based complexity $n(\varepsilon,d)$ for $d$-variate function approximation problems. In the deterministic setting for many unweighted problems the curse of dimensionality…
In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…
Computational complexity is a particularly important objective. The idea of Landauer principle was extended through mapping three classic problems (sorting,ordered searching and max of N unordered numbers) into Maxwell demon thought…