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γ-ABC: Outlier-Robust Approximate Bayesian Computation Based on a Robust Divergence Estimator

Masahiro Fujisawa · Takeshi Teshima · Issei Sato · Masashi Sugiyama


Keywords: [ Applications ] [ Computer Vision ] [ Applications -> Denoising; Theory ] [ Information Theory ] [ Learning Theory and Statistics ] [ Robust Statistics and Machine Learning ]


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 γ-divergence estimator as a data discrepancy measure. We show that our estimator possesses a suitable 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 complexity. Through experiments, we demonstrate that our method achieves significantly higher robustness than existing discrepancy measures.

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