Computational Statistics seminars

A Markov chain can sample effectively from a random or data-informed start even when worst-case initialization mixes slowly. This talk uses weak Poincaré inequalities to analyse that regime, with applications to simulated annealing for spherical spin glasses and to mixtures of log-concave distributions.

Continuum Glauber dynamics samples Gibbs point processes with repulsive interactions, including hard spheres. This talk develops continuous spectral-independence and localization tools to establish spectral gaps and efficient sampling for arbitrary-range repulsive potentials. The approach improves fixed-density packing thresholds and works directly in the continuum rather than discretizing the model.

Score-based generation need not reverse a forward diffusion process. This talk presents an alternative based on Langevin MCMC at a fixed noise level, with effective noise falling as measurements accumulate. Suitable noise choices keep the sampling problems log-concave, and extensions connect the construction to discrete-data generation.

A polynomial-time algorithm samples the Sherrington–Kirkpatrick Gibbs distribution with negligible total-variation error for inverse temperatures below one half. The talk combines stochastic localization, Jarzynski's equality and rejection sampling with covariance and functional-inequality estimates. It also derives a weak Poincaré inequality that simplifies the construction and relates the guarantees to earlier Wasserstein results.

Windowed thinning exactly simulates bouncy-particle and coordinate Zigzag sampling processes by constructing local event-rate envelopes from gradients. For strongly convex, smooth targets, the talk combines this construction with mixing estimates and event-count bounds to derive query-complexity guarantees from a Gaussian cold start, distinguishing full-gradient and coordinate-query costs.

Normalizing Flow Maps learn invertible transports between arbitrary pairs of times while retaining exact density evaluation. This combines few-step generation with likelihoods and sampling in both temporal directions. The talk develops pointwise and distributional consistency objectives, including forward and reverse KL formulations, connecting flow-map regression with likelihood training. Image-generation experiments and equilibrium sampling of small peptides test the approach against earlier normalizing-flow methods.