$\gamma$-ABC: Outlier-Robust Approximate Bayesian Computation Based on a Robust Divergence Estimator

Masahiro Fujisawa; Takeshi Teshima; Issei Sato; Masashi Sugiyama

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arXiv · 2006.07571

$\gamma$-ABC: Outlier-Robust Approximate Bayesian Computation Based on a Robust Divergence Estimator

Masahiro Fujisawa·Takeshi Teshima·Issei Sato·Masashi Sugiyama

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Abstract

Approximate Bayesian computation (ABC) is a likelihood-free inference method that has been employed in various applications. However, ABC can be sensitive to outliers if a data discrepancy measure is chosen inappropriately. In this paper, we propose to use a nearest-neighbor-based $\gamma$-divergence estimator as a data discrepancy measure. We show that our estimator possesses a suitable theoretical robustness property called the redescending property. In addition, our estimator enjoys various desirable properties such as high flexibility, asymptotic unbiasedness, almost sure convergence, and linear-time computational complexity. Through experiments, we demonstrate that our method achieves significantly higher robustness than existing discrepancy measures.

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Masahiro Fujisawa, Takeshi Teshima, Issei Sato, Masashi Sugiyama. 2020-06-13. $\gamma$-ABC: Outlier-Robust Approximate Bayesian Computation Based on a Robust Divergence Estimator. https://arxiv.org/abs/2006.07571

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