Gaussian Process Regression for Maximum Entropy Distribution
Maximum-Entropy Distributions offer an attractive family of probability densities suitable for moment closure problems. Yet finding the Lagrange multipliers which parametrize these distributions, turns out to be a computational bottleneck for practical closure settings. Motivated by recent success of Gaussian processes, we investigate the suitability of Gaussian priors to approximate the Lagrange multipliers as a map of a given set of moments. Examining various kernel functions, the hyperparameters are optimized by maximizing the log-likelihood. The performance of the devised data-driven Maximum-Entropy closure is studied for couple of test cases including relaxation of non-equilibrium distributions governed by Bhatnagar-Gross-Krook and Boltzmann kinetic equations.
Code (0)
등록된 구현이 없습니다.
Tasks
Gaussian ProcessesregressionSimilar Papers 제목 키워드 기반
Deriving the Scaled-Dot-Function via Maximum Likelihood Estimation and Maximum Entropy Approach
In this paper, we present a maximum likelihood estimation approach to determine the value vector in transformer models. We model the sequence of value vectors, key vectors, and the query vector as a sequence of Gaussian …
Maximum Correntropy Criterion with Variable Center
Correntropy is a local similarity measure defined in kernel space and the maximum correntropy criterion (MCC) has been successfully applied in many areas of signal processing and machine learning in recent years. The ker…
PositionMaximum Correntropy Unscented Filter
The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilizing a derivative-free higher-order approximation by approximating a Gaussian distribut…
State EstimationGeneralized Correntropy for Robust Adaptive Filtering
As a robust nonlinear similarity measure in kernel space, correntropy has received increasing attention in domains of machine learning and signal processing. In particular, the maximum correntropy criterion (MCC) has rec…
Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed
Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select appropriate parameters for the covarian…
regression