Sparse mixture models inspired by ANOVA decompositions

Hertrich, Johannes; Ba, Fatima Antarou; Steidl, Gabriele

doi:10.1553/etna_vol55s142

etna

2021

DOI: 10.1553/etna_vol55s142

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Sparse mixture models inspired by ANOVA decompositions

Johannes Hertrich¹,

Fatima Antarou Ba²,

Gabriele Steidl³

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2024

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“…Both decompositions make it possible to analyze the different dimensions and their interactions, and to perform high dimensional integration [16,19] using quadrature methods as well as infinite-dimensional integration [6,19,32]. Further, in [23], we proposed, inspired by the analysis of variance ANOVA decomposition of functions, a Gaussian-Uniform mixture model on the high-dimensional torus which relies on the assumption that the function we wish to approximate can be well explained by limited variable interactions.…”

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Sparse additive function decompositions facing basis transforms

Antarou Ba,

Melnyk,

Wald

et al. 2024

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High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find sparse additive decompositions of functions. In this paper, we are interested in a setting, where these decompositions are not directly sparse, but become so after an appropriate basis transform. Noting that the sparsity of those additive function decompositions is equivalent to the fact that most of its mixed partial derivatives vanish, we can exploit a connection to the underlying function graphs to determine an orthogonal transform that realizes the appropriate basis change. This is done in three steps: we apply singular value decomposition to minimize the number of vertices of the function graph, and joint block diagonalization techniques of families of matrices followed by sparse minimization based on relaxations of the zero "norm" for minimizing the number of edges. For the latter one, we propose and analyze minimization techniques over the manifold of special orthogonal matrices. Various numerical examples illustrate the reliability of our approach for functions having, after a basis transform, a sparse additive decomposition into summands with at most two variables.

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confidence: 99%

Sparse additive function decompositions facing basis transforms

Antarou Ba,

Melnyk,

Wald

et al. 2024

FoDS

Self Cite

View full text Add to dashboard Cite

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Sparse mixture models inspired by ANOVA decompositions

Cited by 1 publication

References 34 publications

Sparse additive function decompositions facing basis transforms

Sparse additive function decompositions facing basis transforms

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