jeune fille à la perle [street art]

transport, diffusions, and sampling

At the Sampling, Transport, and Diffusions workshop at the Flatiron Institute, on Day #2, Marilou Gabrié (École Polytechnique) gave the second introductory lecture on merging sampling and normalising flows targeting the target distribution, when driven by a divergence criterion like KL, that only requires the shape of the target density. I first wondered about ergodicity guarantees in simultaneous MCMC and map training due to the adaptation of the flow but the update of the map only depends on the current particle cloud in (8). From an MCMC perspective, it sounds somewhat paradoxical to see the independent sampler making such an unexpected come-back when considering that no insider information is available about the (complex) posterior to drive the [what-you-get-is-what-you-see] construction of the transport map. However, the proposed approach superposed local (random-walk like) and global (transport) proposals in Algorithm 1.

Qiang Liu followed on learning transport maps, with the  Interesting notion of causalizing a graph by removing intersections (which are impossible for an ODE, as discussed by Eric Vanden-Eijden’s talk yesterday) through  coupling. Which underlies his notion of rectified flows. Possibly connecting with the next lightning talk by Jonathan Weare on spurious modes created by a variational Monte Carlo sampler and the use of stochastic gradient, corrected by (case-dependent?) regularisation.

Then came a whole series of MCMC talks!

Sam Livingstone spoke on Barker’s proposal (an incoming Biometrika paper!) as part of a general class of transforms g of the MH ratio, using jump processes based on a nasty normalising constant related with g (tractable for the original Barker algorithm). I then realised I had missed his StatSci paper on how to speak to statistical physics researchers!

Charles Margossian spoke about using a massive number of short parallel runs (many-short-chain regime) from a recent paper written with Aki,  Andrew, and Lionel Riou-Durand (Warwick) among others. Which brings us back to the challenge of producing convergence diagnostics and precisely the Gelman-Rubin R statistic or its recent nR avatar (with its linear limitations and dependence on parameterisation, as opposed to fuller distributional criteria). The core of the approach is in using blocks of GPUs to improve and speed-up the estimation of the between-chain variance. (D for R².) I still wonder at a waste of simulations / computing power resulting from stopping the runs almost immediately after warm-up is over, since reaching the stationary regime or an approximation thereof should be exploited more efficiently. (Starting from a minimal discrepancy sample would also improve efficiency.)

Lu Zhang also talked on the issue of cutting down warmup, presenting a paper co-authored with Bob, Andrew, and Aki, recommending Laplace / variational approximations for reaching faster high-posterior-density regions, using an algorithm called Pathfinder that relies on ELBO checks to counter poor performances of Laplace approximations. In the spirit of the workshop, it could be profitable to further transform / push-forward the outcome by a transport map.

Yuling Yao (of stacking and Pareto smoothing fame!) gave an original and challenging (in a positive sense) talk on the many ways of bridging densities [linked with the remark he shared with me the day before] and their statistical significance. Questioning our usual reliance on arithmetic or geometric mixtures. Ignoring computational issues, selecting a bridging pattern sounds not different from choosing a parameterised family of embedding distributions. This new typology of models can then be endowed with properties that are more or less appealing. (Occurences of the Hyvärinen score and our mixtestin perspective in the talk!)

Miranda Holmes-Cerfon talked about MCMC on stratification (illustrated by this beautiful picture of nanoparticle random walks). Which means sampling under varying constraints and dimensions with associated densities under the respective Hausdorff measures. This sounds like a perfect setting for reversible jump and in a sense it is, as mentioned in the talks. Except that the moves between manifolds are driven by the proximity to said manifold, helping with a higher acceptance rate, and making the proposals easier to construct since projections (or the reverses) have a physical meaning. (But I could not tell from the talk why the approach was seemingly escaping the symmetry constraint set by Peter Green’s RJMCMC on the reciprocal moves between two given manifolds).

Montréal street art [jatp]

il sortit de la maison au moment où l’été commençait [jatp]

day two at ISBA 22

Still woke up early too early, which let me go for a long run in Mont Royal (which felt almost immediately familiar from earlier runs at MCM 2017!) at dawn and at a pleasant temperature (but missed the top bagel bakery on the way back!). Skipped the morning plenary lectures to complete recommendation letters and finishing a paper submission. But had a terrific lunch with a good friend I had not seen in Covid-times, at a local branch of Kinton Ramen which I already enjoyed in Vancouver as my Airbnb was located on top of it.

I chaired the afternoon Bayesian computations session with Onur Teymur presenting the general spirit of his Neurips 21 paper on black box probabilistic numerics. Mentioning that a new textbook on the topic by Phillip Henning, Michael Osborne, and Hans Kersting had appeared today! The second talk was by Laura Bondi who discussed an ABC model choice approach to assess breast cancer screening. With enough missing data (out of 78051 women followed over 12 years) to lead to an intractable likelihood. Starting with vanilla ABC using 32 summaries and moving to our random forest approach. Unsurprisingly concluding with different top models, but not characterising the identifiability provided by the choice of the summaries. The third talk was by Ryan Chan (fresh Warwick PhD recipient), about a Fusion divide-and-conquer approach that avoids the approximation of earlier approaches. In particular he uses a clever accept-reject algorithm to generate a product of densities using the component densities. A nice trick that Murray explained to me while visiting in Paris lg ast month. (The approach appears to be parameterisation dependent.) The final talk was by Umberto Picchini and in a sort the synthetic likelihood mirror of Massi’s talk yesterday, in the sense of constructing a guided proposal relying on observed summaries. If not comparing both approaches on a given toy like the g-and-k distribution.