Johannes Hertrich,
Fatima Antarou Ba,
Gabriele Steidl
S. 142 - 168
doi:
10.1553/etna_vol55s142
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol55s142
Abstract:
Inspired by the analysis of variance (ANOVA) decomposition of functions, we propose a Gaussian-uniform mixture model on the high-dimensional torus which relies on the assumption that the function that we wish to approximate can be well explained by limited variable interactions. We consider three model approaches, namely wrapped Gaussians, diagonal wrapped Gaussians, and products of von Mises distributions. The sparsity of the mixture model is ensured by the fact that its summands are products of Gaussian-like density functions acting on low-dimensional spaces and uniform probability densities defined on the remaining directions. To learn such a sparse mixture model from given samples, we propose an objective function consisting of the negative log-likelihood function of the mixture model and a regularizer that penalizes the number of its summands. For minimizing this functional we combine the Expectation Maximization algorithm with a proximal step that takes the regularizer into account. To decide which summands of the mixture model are important, we apply a Kolmogorov-Smirnov test. Numerical examples demonstrate the performance of our approach.
sparse mixture models, ANOVA decomposition, wrapped Gaussian distribution, von Mises distribution, approximation of high-dimensional probability density functions, Kolmogorov-Smirnov test
Published Online:
2021/11/18 10:27:50
Object Identifier:
0xc1aa5576 0x003d0113
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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