Related papers: Sample complexity of Schr\"odinger potential estim…

We consider the problem of sampling from a probability distribution $\pi$ which admits a density w.r.t. a dominating measure. It is well known that this can be written as an optimisation problem over the space of probability distributions…

The Kullback-Leibler cluster entropy $\mathcal{D_{C}}[P \| Q] $ is evaluated for the empirical and model probability distributions $P$ and $Q$ of the clusters formed in the realized volatility time series of five assets (SP\&500, NASDAQ,…

We study the Kullback--Leibler (KL) divergence approximation theory of Gaussian mixture models (GMMs) by isolating an abstract mechanism behind several necessary-and-sufficient statements. The necessity direction is universal: if a density…

The Schr\"odinger bridge problem (SBP) seeks to find the measure $\hat{\mathbf{P}}$ on a certain path space which interpolates between state-space distributions $\rho_0$ at time $0$ and $\rho_T$ at time $T$ while minimizing the KL…

We present a regularized finite difference method for the logarithmic Schr\"odinger equation (LogSE) and establish its error bound. Due to the blow-up of the logarithmic nonlinearity, i.e. $\ln \rho\to -\infty$ when $\rho\rightarrow 0^+$…

For training an encoder network to perform amortized variational inference, the Kullback-Leibler (KL) divergence from the exact posterior to its approximation, known as the inclusive or forward KL, is an increasingly popular choice of…

We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. In this paper, we build on previous work combining Schr\"odinger bridges and plug & play Langevin…

We study the problem of nonnegative rank-one approximation of a nonnegative tensor, and show that the globally optimal solution that minimizes the generalized Kullback-Leibler divergence can be efficiently obtained, i.e., it is not NP-hard.…

Schr\"odinger bridges (SBs) provide an elegant framework for modeling the temporal evolution of populations in physical, chemical, or biological systems. Such natural processes are commonly subject to changes in population size over time…

We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint…

We study the problem of finding global minimizers of $V(x):\mathbb{R}^d\rightarrow\mathbb{R}$ approximately via sampling from a probability distribution $\mu_{\sigma}$ with density $p_{\sigma}(x)=\dfrac{\exp(-V(x)/\sigma)}{\int_{\mathbb…

We study empirical Bayes (EB) predictive density estimation in linear mixed models (LMMs) with large number of units, which induce a high dimensional random effects space. Focusing on Kullback Leibler (KL) risk minimization, we develop a…

Homotopy approaches to Bayesian inference have found widespread use especially if the Kullback-Leibler divergence between the prior and the posterior distribution is large. Here we extend one of these homotopy approach to include an…

In this paper, we propose to solve a regularized distributionally robust learning problem in the decentralized setting, taking into account the data distribution shift. By adding a Kullback-Liebler regularization function to the robust…

We investigate the kinetic Schr\"odinger problem, obtained considering Langevin dynamics instead of Brownian motion in Schr\"odinger's thought experiment. Under a quasilinearity assumption we establish exponential entropic turnpike…

We propose a shrinkage procedure for simultaneous variable selection and estimation in generalized linear models (GLMs) with an explicit predictive motivation. The procedure estimates the coefficients by minimizing the Kullback-Leibler…

Kullback Leibler (KL) control problems allow for efficient computation of optimal control by solving a principal eigenvector problem. However, direct applicability of such framework to continuous state-action systems is limited. In this…

We characterize Martin-L\"of randomness and Schnorr randomness in terms of the merging of opinions, along the lines of the Blackwell-Dubins Theorem. After setting up a general framework for defining notions of merging randomness, we focus…

Symmetrized Kullback-Leibler (KL) information (\(I_{\mathrm{SKL}}\)), which symmetrizes the traditional mutual information by integrating Lautum information, has been shown as a critical quantity in communication~\cite{aminian2015capacity}…

We consider a Schr\"odinger bridge problem where the Markov process is subject to parameter perturbations, forming an ensemble of systems. Our objective is to steer this ensemble from the initial distribution to the final distribution using…