Model parameter learning using Kullback–Leibler divergence

Chungwei Lin, Tim K. Marks, Milutin Pajovic, Shinji Watanabe, Chih kuan Tung

研究成果: Article査読

抄録

In this paper, we address the following problem: For a given set of spin configurations whose probability distribution is of the Boltzmann type, how do we determine the model coupling parameters? We demonstrate that directly minimizing the Kullback–Leibler divergence is an efficient method. We test this method against the Ising and XY models on the one-dimensional (1D) and two-dimensional (2D) lattices, and provide two estimators to quantify the model quality. We apply this method to two types of problems. First, we apply it to the real-space renormalization group (RG). We find that the obtained RG flow is sufficiently good for determining the phase boundary (within 1% of the exact result) and the critical point, but not accurate enough for critical exponents. The proposed method provides a simple way to numerically estimate amplitudes of the interactions typically truncated in the real-space RG procedure. Second, we apply this method to the dynamical system composed of self-propelled particles, where we extract the parameter of a statistical model (a generalized XY model) from a dynamical system described by the Viscek model. We are able to obtain reasonable coupling values corresponding to different noise strengths of the Viscek model. Our method is thus able to provide quantitative analysis of dynamical systems composed of self-propelled particles.

本文言語English
ページ(範囲)549-559
ページ数11
ジャーナルPhysica A: Statistical Mechanics and its Applications
491
DOI
出版ステータスPublished - 2018 2 1
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率
  • 凝縮系物理学

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