After the (exciting) variety and spread of ISBA²⁶, here we are at much more focussed (and single-track), if equally exciting, workshop at the ISM. (With many participants from ISBA²⁶.)
On Saturday afternoon, Ajay Jasra talked about Particle filtering for state-space models with low, degenerate noise, with specific measure issues I did not really get, since the manifold attached to the noise was known, but the projected density may prove a challenge. Manifolds were also central to Kenji Fukumizu’s talk on Learning manifold structure and density with score-based models learning scores as projectors to the manifold, although it was unclear to me how this was possible when the manifold is unknown. Christophe Andrieu presented Geometry informed selection in multiple proposal MCMC which stems from an early multi-proposal (1998) proposal by Radford Neal and uses a multivariate ranking procedure to quantify a measure of surprise for the current Markov chain value within the proposed ones. The crux for the efficiency of the approach may be in the choice of this ranking procedure. And Maria De Iorio talked about Efficient MCMC via similarity-driven proposals for discrete support targets, with similarities with ABC.
Completed with a human sized poster session where I reconnected with Spanish friends I had not seen for ages (by missing OBayes meetings).
On (pleasantly rainy) Sunday morning, Federica Milinanni detailled her Rapid mixing of stereographic MCMC for heavy-tailed sampling, essentially the same content as in Nagoya last FRiday, with a novel sub-Cauchy projection supposed to explore heavy tails better: while the regular stereographic projection turns the t-distribution with d degrees of freedom into a Uniform on the hypersphere, a sub-Cauchy projection turns the Cauchy into this uniform. In the privacy session I organised, Hongsheng Dai, member of our ERC Synergy project, presented an Online federated learning framework for classification, using DP as a criterion and achieving by adding noise to the loss function at each occurrence of the data production. Surprisingly increasing with the number of occurrences, not so much since the objective function keeps calling
Stefano Favaro described his Bayesian nonparametric privacy-preserving synthetic data generation method (for discrete data) that connects privacy protection and information preservation. (Incidentally I was unaware of the σ parameter of the Pitman-Yor process, which allows for a finite support when σ<0, but I cannot fathom the appeal of this extension, given the complete lack of connection between the positive and negative cases.) Surprisingly, non-parametric prediction does worse in terms of privacy, if not so surprising with discrete data since the predictive actually put weight on every datapoint. Resorting to mechanism informativity by Wasserman and Zhou (2010) (with a surprise mention of my friend Arnaud Guilin!). And Joshua Bon gave his Persuasive Privacy talk of last Tuesday (to be re-repeated two days later at ICML²⁶ in Seoul!). Except for changing the audience game from croissants to sumo wrestlers! (What will it be in Seoul!?) And adding much more details on the foundational elements of persuasive privacy.
The poster session was similarly enjoyable, even though I did not manage to get through all posters.
