**A**t BNP13, Brian Trippe presented the AISTAT 2022 paper he recently wrote with Tin D. Nguyen and Tamara Broderick. Which made me read their 2021 paper on the topic. There, they note that coupling may prove challenging, which they blame on label switching. Considering a naïve Gibbs sampler on the space of partitions, meaning allocating each data-point to one of the existing partitions or to a singleton, they construct an optimal transport coupling under Hamming distance. Which appears to be achievable in O(NK³log{K}), if K is the maximal number of partitions among both chains. The paper does not goes deeply into the implementation, which involves [to quote] (a) *computing* the* distances between each pair of partitions in the Cartesian product of supports of the Gibbs conditionals* and (b) *solving the optimal transport problem*. Except in the appendix where the book-keeping necessary to achieve O(K²) for pairwise distances and the remaining complexity follows from the standard Orlin’s algorithm. What remains unclear from the paper is that, while the chains couple faster (fastest?), the resulting estimators do not necessarily improve upon budget-equivalent alternatives. (The reason for the failure of the single chain in Figure 2 is hard to fathom.)

## Archive for AISTATS 2022

## coupling for the Gibbs sampler

Posted in Books, Mountains, pictures, Running, Statistics, Travel, University life with tags AISTATS 2022, BNP13, Hamming distance, label switching, Lago Llanquihue, maximal coupling, optimal transport, Orlin's algorithm, Orsono volcano, partition, single chain on November 27, 2022 by xi'an## nonparametric ABC [seminar]

Posted in pictures, Statistics, University life with tags ABC, AISTATS 2022, approximate Bayesian inference, Bayesian nonparametrics, g-and-k distributions, maximum mean discrepancy, misspecified model, One World ABC Seminar, RKHS, robustness, University of Warwick, WABC, Wasserstein distance, webinar on June 3, 2022 by xi'an**P**uzzle: How do you run ABC when you mistrust the model?! We somewhat considered this question in our misspecified ABC paper with David and Judith. An AISTATS 2022 paper by Harita Dellaporta (Warwick), Jeremias Knoblauch, Theodoros Damoulas (Warwick), and François-Xavier Briol (formerly Warwick) is addressing this same question and Harita presented the paper at the One World ABC webinar yesterday.

It is inspired from Lyddon, Walker & Holmes (2018), who place a nonparametric prior on the generating model, in top of the assumed parametric model (with an intractable likelihood). This induces a push-forward prior on the pseudo-true parameter, that is, the value that brings the parametric family the closest possible to the true distribution of the data. Here defined as a minimum distance parameter, the maximum mean discrepancy (MMD). Choosing RKHS framework allows for a practical implementation, resorting to simulations for posterior realisations from a Dirichlet posterior and from the parametric model, and stochastic gradient for computing the pseudo-true parameter, which may prove somewhat heavy in terms of computing cost.

The paper also containts a consistency result in an ε-contaminated setting (contamination of the assumed parametric family). Comparisons like the above with a fully parametric Wasserstein-ABC approach show that this alter resists better misspecification, as could be expected since the later is not constructed for that purpose.

*Next talk is on 23 June by Cosma Shalizi.*