Related papers: Relative Entropy Minimization over Hilbert Spaces …
In this paper we approximate the radiative transfer equations by the method of moments, constructing mesoscopic approximations of arbitrary order of the otherwise microscopic system. To define the necessary closure a minimum entropy…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
We consider the problem of approximating a general Gaussian location mixture by finite mixtures. The minimum order of finite mixtures that achieve a prescribed accuracy (measured by various $f$-divergences) is determined within constant…
The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are interested in designing numerical methods which are robust…
We initiate a study of the following problem: Given a continuous domain $\Omega$ along with its convex hull $\mathcal{K}$, a point $A \in \mathcal{K}$ and a prior measure $\mu$ on $\Omega$, find the probability density over $\Omega$ whose…
Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…
Contemporary global optimization algorithms are based on local measures of utility, rather than a probability measure over location and value of the optimum. They thus attempt to collect low function values, not to learn about the optimum.…
Minimization of the (regularized) entropy of classification probabilities is a versatile class of discriminative clustering methods. The classification probabilities are usually defined through the use of some classical losses from…
We introduce a natural definition of $L^p$-convergence of maps, $p \ge 1$, in the case where the domain is a convergent sequence of measured metric space with respect to the measured Gromov-Hausdorff topology and the target is a…
We apply the replica analysis established by Gardner to the multi-constraint continuous knapsack problem,which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large…
We revisit the classical problem of inverting dimension-reducing linear mappings using the maximum entropy (MaxEnt) criterion. In the literature, solutions are problem-dependent, inconsistent, and use different entropy measures. We propose…
We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of ``almost Gibbsian measures'' (almost sure continuity…
We establish a dimension-free improvement of Talagrand's Gaussian transport-entropy inequality, under the assumption that the measures satisfy a Poincar\'e inequality. We also study stability of the inequality, in terms of relative entropy,…
We show that, for vector spaces in which distance measurement is performed using a gauge, the existence of best coapproximations in $1$-codimensional closed linear subspaces implies in dimensions $\geq 2$ that the gauge is a norm, and in…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
Despite the performance advantages of modern sampling-based motion planners, solving high dimensional planning problems in near real-time remains a challenge. Applications include hyper-redundant manipulators, snake-like and humanoid…
We introduce a new generalization of relative entropy to non-negative vectors with sums $\gt 1$. We show in a purely combinatorial setting, with no probabilistic considerations, that in the presence of linear constraints defining a convex…
In the framework of abstract linear inverse problems in infinitedimensional Hilbert space we discuss generic convergence behaviours of approximate solutions determined by means of general projection methods, namely outside the standard…
While one-dimensional Markov processes are well understood, going to higher dimensions there are only a few analytically solved Ising-like models, in practice requiring to use relatively costly, uncontrollable and inaccurate Monte-Carlo…