The paper proves polynomial mixing time upper bounds for three data augmentation algorithms (ProbitDA, LogitDA, LassoDA) with explicit dependence on design matrix, prior, n, and d.
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Proves space-time LSI and hypocoercive hypercontractivity for underdamped Langevin dynamics, giving Rényi divergence decay at rate O(sqrt(rho)) under tuned friction.
Parallel Picard-map algorithms for zeroth-order Random Walk Metropolis achieve O(sqrt(d)) parallel iterations with O(sqrt(d)) processors on log-concave distributions in d dimensions.
Novel splitting scheme for kinetic Langevin sampling with exact harmonic integrator yields L2-Wasserstein convergence rates matching continuous dynamics and non-asymptotic error bounds for strongly log-concave targets.
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Space-Time Log-Sobolev Inequality and Hypocoercive Hypercontractivity for Underdamped Langevin Dynamics
Proves space-time LSI and hypocoercive hypercontractivity for underdamped Langevin dynamics, giving Rényi divergence decay at rate O(sqrt(rho)) under tuned friction.
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Convergence and non-asymptotic error analysis for kinetic Langevin samplers using the exact harmonic Langevin integrator
Novel splitting scheme for kinetic Langevin sampling with exact harmonic integrator yields L2-Wasserstein convergence rates matching continuous dynamics and non-asymptotic error bounds for strongly log-concave targets.