$γ$-ABC: Outlier-Robust Approximate Bayesian Computation Based on a Robust Divergence Estimator
This addresses outlier robustness in likelihood-free inference for applications in statistics and machine learning, representing an incremental improvement.
The paper tackles the sensitivity of Approximate Bayesian Computation (ABC) to outliers by proposing a nearest-neighbor-based γ-divergence estimator as a data discrepancy measure, achieving significantly higher robustness than existing measures in experiments.
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 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.