γ-ABC

An AISTATS 2021 paper by Masahiro Fujisawa,Takeshi Teshima, Issei Sato and Masashi Sugiyama (RIKEN, Tokyo) just appeared on arXiv.  (AISTATS 2021 is again virtual this year.)

“ABC can be sensitive to outliers if a data discrepancy measure is chosen inappropriately (…) In this paper, we propose a novel outlier-robust and computationally-efficient discrepancy measure based on the γ-divergence”

The focus is on measure of robustness for ABC distances as those can be lethal if insufficient summarisation is used. (Note that a referenced paper by Erlis Ruli, Nicola Sartori and Laura Ventura from Padova appeared last year on robust ABC.) The current approach mixes the γ-divergence of Fujisawa and Eguchi, with a k-nearest neighbour density estimator. Which may not prove too costly, of order O(n log n), but also may be a poor if robust approximation, even if it provides an asymptotic unbiasedness and almost surely convergent approximation. These properties are those established in the paper, which only demonstrates convergence in the sample size n to an ABC approximation with the true γ-divergence but with a fixed tolerance ε, when the most recent results are rather concerned with the rates of convergence of ε(n) to zero. (An extensive simulation section compares this approach with several ABC alternatives, incl. ours using the Wasserstein distance. If I read the comparison graphs properly, it does not look as if there is a huge discrepancy between the two approaches under no contamination.) Incidentally, the paper contains a substantial survey section and has a massive reference list, if missing the publication more than a year earlier of our Wasserstein paper in Series B.