high-dimensional stochastic simulation and optimisation in image processing [day #3]

Last and maybe most exciting day of the “High-dimensional Stochastic Simulation and Optimisation in Image Processing” in Bristol as it was exclusively about simulation (MCMC) methods. Except my own talk on ABC. And Peter Green’s on consistency of Bayesian inference in non-regular models. The talks today were indeed about using convex optimisation devices to speed up MCMC algorithms with tools that were entirely new to me, like the Moreau transform discussed by Marcelo Pereyra. Or using auxiliary variables à la RJMCMC to bypass expensive Choleski decompositions. Or optimisation steps from one dual space to the original space for the same reason. Or using pseudo-gradients on partly differentiable functions in the talk by Sylvain Lecorff on a paper commented earlier in the ‘Og. I particularly liked the notion of Moreau regularisation that leads to more efficient Langevin algorithms when the target is not regular enough. Actually, the discretised diffusion itself may be geometrically ergodic without the corrective step of the Metropolis-Hastings acceptance. This obviously begs the question of an extension to Hamiltonian Monte Carlo. And to multimodal targets, possibly requiring as many normalisation factors as there are modes. So, in fine, a highly informative workshop, with the perfect size and the perfect crowd (which happened to be predominantly French, albeit from a community I did not have the opportunity to practice previously). Massive kudos to Marcello for putting this workshop together, esp. on a week where family major happy events should have kept him at home!

As the workshop ended up in mid-afternoon, I had plenty of time for a long run with Florence Forbes down to the Avon river and back up among the deers of Ashton Court, avoiding most of the rain, all of the mountain bikes on a bike trail that sounded like trail running practice, and building enough of an appetite for the South Indian cooking of the nearby Thali Café. Brilliant!

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