A new episode of our mostly Monte Carlo seminar, very soon coming near you (if in Paris):
On Friday 13/02/26, from 3-5pm at PariSanté Campus
15h00: Pierre Del Moral (INRIA, Bordeaux)
On the Kantorovich contraction of Markov semigroup
We present a novel operator theoretic framework to study the contraction properties of Markov semigroups with respect to a general class of Kantorovich semi-distances, which notably includes Wasserstein distances. This rather simple contraction cost framework combines standard Lyapunov techniques with local contraction conditions. Our results can be applied to both discrete time and continuous time Markov semigroups, and we illustrate their wide applicability in the context of (i) Markov transitions on models with boundary states, including bounded domains with entrance boundaries, (ii) operator products of a Markov kernel and its adjoint, including two-block-type Gibbs samplers, (iii) iterated random functions and (iv) diffusion models, including overdampted Langevin diffusion with convex at infinity potentials.
16h00: Bob Carpenter (Flatiron Institute, New York)
GIST, WALNUTS, and Continuous Nutpie: mass-matrix and step-size adaptation for Hamiltonian Monte Carlo
I will introduce Gibbs self tuning (GIST), our new technique for coupling tuning parameters and conditionally Gibbs-sampling them per iteration in Hamiltonian Monte Carlo. Then I will turn to the within-orbit adaptive NUTS (WALNUTS) sampler, which adapts the step size every leapfrog step in order to conserve the Hamiltonian. Empirical evaluations on varying multi-scale target distributions, including Neal’s funnel and the Stock-Watson stochastic volatility time-series model, demonstrate that WALNUTS achieves substantial improvements in sampling efficiency and robustness. I will review the Nutpie mass-matrix adaptation scheme, which is designed to minimize Fisher divergence by estimating the mass matrix as the geometric midpoint (aka barycenter) between the inverse covariance of the draws and the covariance of the scores of the draws. Then I will describe a continuously adapting version that adapts per iteration by continuously discounting the past rather than updating in fixed blocks. I will also show how the Adam optimizer outperforms dual averaging for step-size adaptation. I will conclude by considering a lock-free multi-threading implementation that automatically monitors adaptation and sampling for convergence for automatic stopping.
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