12 papers
Weak Poincaré Inequalities via Approximate Stochastic Localization: Application to Sampling the Sherrington-Kirkpatrick Model
Ewan Davies, Holden Lee, Juspreet Singh Sandhu +1
We develop a new method for proving a weak functional inequality by first proving it for a sufficiently regular sequence of distributions approximating the stochastic localization…
Potential Hessian Ascent III: Sampling the Sherrington--Kirkpatrick Model at Beta < 1/2
Ewan Davies, Holden Lee, Juspreet Singh Sandhu +1
We give a polynomial-time algorithm to sample from the Gibbs measure of the Sherrington-Kirkpatrick model with negligible total-variation distance (TVD) error up to inverse tempera…
Fast Mixing of Data Augmentation Algorithms: Bayesian Probit, Logit, and Lasso Regression
Holden Lee, Kexin Zhang
We propose using a modified conductance-based method to study the mixing time of an important class of two-block Gibbs samplers, the data augmentation (DA) algorithm. %, which is o…
Convergence Bounds for Sequential Monte Carlo on Multimodal Distributions using Soft Decomposition
Holden Lee, Matheau Santana-Gijzen
We prove bounds on the variance of a function under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm, with time complexity depending…
Sampling from multimodal distributions with warm starts: Non-asymptotic bounds for the Reweighted Annealed Leap-Point Sampler
Holden Lee, Matheau Santana-Gijzen
Sampling from multimodal distributions is a central challenge in Bayesian inference and machine learning. In light of hardness results for sampling -- classical MCMC methods, even…
Mixing of general biased adjacent transposition chains
Reza Gheissari, Holden Lee, Eric Vigoda
We analyze the general biased adjacent transposition shuffle process, which is a well-studied Markov chain on the symmetric group . In each step, an adjacent pair of elements…