Archive for Rademacher complexity

BayesComp²³ [aka MCMski⁶]

Posted in Books, Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , on March 20, 2023 by xi'an

The main BayesComp meeting started right after the ABC workshop and went on at a grueling pace, and offered a constant conundrum as to which of the four sessions to attend, the more when trying to enjoy some outdoor activity during the lunch breaks. My overall feeling is that it went on too fast, too quickly! Here are some quick and haphazard notes from some of the talks I attended, as for instance the practical parallelisation of an SMC algorithm by Adrien Corenflos, the advances made by Giacommo Zanella on using Bayesian asymptotics to assess robustness of Gibbs samplers to the dimension of the data (although with no assessment of the ensuing time requirements), a nice session on simulated annealing, from black holes to Alps (if the wrong mountain chain for Levi), and the central role of contrastive learning à la Geyer (1994) in the GAN talks of Veronika Rockova and Éric Moulines. Victor  Elvira delivered an enthusiastic talk on our massively recycled importance on-going project that we need to complete asap!

While their earlier arXived paper was on my reading list, I was quite excited by Nicolas Chopin’s (along with Mathieu Gerber) work on some quadrature stabilisation that is not QMC (but not too far either), with stratification over the unit cube (after a possible reparameterisation) requiring more evaluations, plus a sort of pulled-by-its-own-bootstrap control variate, but beating regular Monte Carlo in terms of convergence rate and practical precision (if accepting a large simulation budget from the start). A difficulty common to all (?) stratification proposals is that it does not readily applies to highly concentrated functions.

I chaired the lightning talks session, which were 3mn one-slide snapshots about some incoming posters selected by the scientific committee. While I appreciated the entry into the poster session, the more because it was quite crowded and busy, if full of interesting results, and enjoyed the slide solely made of “0.234”, I regret that not all poster presenters were not given the same opportunity (although I am unclear about which format would have permitted this) and that it did not attract more attendees as it took place in parallel with other sessions.

In a not-solely-ABC session, I appreciated Sirio Legramanti speaking on comparing different distance measures via Rademacher complexity, highlighting that some distances are not robust, incl. for instance some (all?) Wasserstein distances that are not defined for heavy tailed distributions like the Cauchy distribution. And using the mean as a summary statistic in such heavy tail settings comes as an issue, since the distance between simulated and observed means does not decrease in variance with the sample size, with the practical difficulty that the problem is hard to detect on real (misspecified) data since the true distribution behing (if any) is unknown. Would that imply that only intrinsic distances like maximum mean discrepancy or Kolmogorov-Smirnov are the only reasonable choices in misspecified settings?! While, in the ABC session, Jeremiah went back to this role of distances for generalised Bayesian inference, replacing likelihood by scoring rule, and requirement for Monte Carlo approximation (but is approximating an approximation that a terrible thing?!). I also discussed briefly with Alejandra Avalos on her use of pseudo-likelihoods in Ising models, which, while not the original model, is nonetheless a model and therefore to taken as such rather than as approximation.

I also enjoyed Gregor Kastner’s work on Bayesian prediction for a city (Milano) planning agent-based model relying on cell phone activities, which reminded me at a superficial level of a similar exploitation of cell usage in an attraction park in Singapore Steve Fienberg told me about during his last sabbatical in Paris.

In conclusion, an exciting meeting that should have stretched a whole week (or taken place in a less congenial environment!). The call for organising BayesComp 2025 is still open, by the way.


day one at ISBA 22

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , on June 29, 2022 by xi'an

Started the day with a much appreciated swimming practice in the [alas warm⁺⁺⁺] outdoor 50m pool on the Island with no one but me in the slooow lane. And had my first ride with the biXi system, surprised at having to queue behind other bikes at red lights! More significantly, it was a great feeling to reunite at last with so many friends I had not met for more than two years!!!

My friend Adrian Raftery gave the very first plenary lecture on his work on the Bayesian approach to long-term population projections, which was recently  a work censored by some US States, then counter-censored by the Supreme Court [too busy to kill Roe v. Wade!]. Great to see the use of Bayesian methods validated by the UN Population Division [with at least one branch of the UN

Stephen Lauritzen returning to de Finetti notion of a model as something not real or true at all, back to exchangeability. Making me wonder when exchangeability is more than a convenient assumption leading to the Hewitt-Savage theorem. And sufficiency. I mean, without falling into a Keynesian fallacy, each point of the sample has unique specificities that cannot be taken into account in an exchangeable model. Nice to hear some measure theory, though!!! Plus a comment on the median never being sufficient, recouping an older (and presumably not original) point of mine. Stephen’s (or Fisher’s?) argument being that the median cannot be recursively computed!

Antonietta Mira and I had our ABC session this afternoon with Cecilia Viscardi, Sirio Legramanti, and Massimiliano Tamborino (Warwick) as speakers. Cecilia linked ABC with normalising flows, in collaboration with Dennis Prangle (whose earlier paper on this connection was presented as the first One World ABC seminar). Thus using past simulations to approximate the posterior by a neural network, possibly with a significant increase in computing time when compared with more rudimentary SMC-ABC methods in larger dimensions. Sirio considered summary-free ABC based on discrepancies like Rademacher complexity. Which more or less contains MMD, Kullback-Leibler, Wasserstein and more, although it seems to be dependent on the parameterisation of the observations. An interesting opening at the end was that this approach could apply to non iid settings. Massi presented a paper coauthored with Umberto that had just been arXived. On sequential ABC with a dependence on the summary statistic (hence guided). Further bringing copulas into the game, although this forces another choice [for the marginals] in the method.

Tamara Broderick talked about a puzzling leverage effect of some observations in economic studies where a tiny portion of individuals may modify the significance or the sign of a coefficient, for which I cannot tell whether the data or the reliance on statistical significance are to blame. Robert Kohn presented mixture-of-Gaussian copulas [not to be confused with mixture of Gaussian-copulas!] and Nancy Reid concluded my first [and somewhat exhausting!] day at ISBA with a BFF talk on the different statistical paradigms take on confidence (for which the notion of calibration seems to remain frequentist).

Side comments: First, most people in the conference are wearing masks, which is great! Also, I find it hard to read slides from the screen, which I presume is an age issue (?!) Even more aside, I had Korean lunch in a place that refused to serve me a glass of water, which I find amazing.

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