At 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.)
While in Puerto Varas for BNP13, I tried to summit the nearby 
When we started again the wind had strengthened with the incoming dawn, rising to a point where we could hardly stand up to it, and our guide eventually decided to turn back, as it was only to get worse in the remaining 600m to the top, confirming the earlier prediction of 70km/hour winds… Yichin was of the same opinion and hence we reluctantly turned back down to the bottom of the slope, with the wind mostly on our back and a pleasant steady gradient descent. (Although my tights are still sensitive three days after the climb!) Surprisingly I was not feeling particularly cold (and with the right face protection my nose was not close to frozen, which happened on Monte Rosa in 2016). Even after seeing my best North Face mitt been blown away within a second of loosing grip of it! (Anyone with a spare left hand down mitt?! Because it had to be 
Obviously, this was quite disappointing as I had planned the climb for weeks, brought all the layers to face a potential -20⁰ windchill, was in good enough shape, did not feel any 
