Algorithms for Kullback--Leibler Approximation of Probability Measures in Infinite Dimensions
نویسندگان
چکیده
منابع مشابه
Algorithms for Kullback-Leibler Approximation of Probability Measures in Infinite Dimensions
In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the Kullback–Leibler divergence as a distance and find the best Gaussian approximation by minimizing this distance. It then follows that the approximate Gaussia...
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In a variety of applications it is important to extract information from a probability measure μ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and (possibly conditioned) continuous time Markov processes. It may then be of interest to find a measure ν, from within a simple class of measures, which approximates μ. This problem is studied in the case ...
متن کاملThe Kullback-Leibler Information Function for Infinite Measures
Victor Bakhtin 1,* and Edvard Sokal 2 1 Department of Mathematics, IT and Landscape Architecture, John Paul II Catholic University of Lublin, Konstantynuv Str. 1H, 20-708 Lublin, Poland 2 Department of Mechanics and Mathematics, Belarusian State University, Nezavisimosti Ave. 4, 220030 Minsk, Belarus; [email protected] * Correspondence: [email protected] or [email protected]; Tel.: +375...
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We introduce a Kullback-Leibler type distance between spectral density functions of stationary stochastic processes and solve the problem of optimal approximation of a given spectral density Ψ by one that is consistent with prescribed second-order statistics. In general, such statistics are expressed as the state covariance of a linear filter driven by a stochastic process whose spectral densit...
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In this paper, we study a matricial version of a generalized moment problem with degree constraint. We introduce a new metric on multivariable spectral densities induced by the family of their spectral factors, which, in the scalar case, reduces to the Hellinger distance. We solve the corresponding constrained optimization problem via duality theory. A highly nontrivial existence theorem for th...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2015
ISSN: 1064-8275,1095-7197
DOI: 10.1137/14098171x