14 papers
Sharp dimensional analysis of midpoint methods for Langevin sampling
Fan Chen, Sinho Chewi, Jianfeng Lu +1
We study deterministic and randomized midpoint discretizations of Langevin dynamics for a target , where and . To achi…
High-accuracy simulation of Picard HMC, part I: Gaussian cloud correction
Fan Chen, Sinho Chewi, Jianfeng Lu +1
We study the problem of sampling from a continuous density on , where has a -Lipschitz gradient and satisfies a loga…
Smoothed Picard Hamiltonian Monte Carlo
Fan Chen, Sinho Chewi, Jianfeng Lu +1
We develop a new low-accuracy sampler, called smoothed Picard Hamiltonian Monte Carlo, which combines Gaussian smoothing, Picard iteration, and higher-order discretization. For a l…
Accelerated High-Accuracy Sampling from a Warm Start via the Proximal Bouncy Particle Sampler
Fan Chen, Sinho Chewi, Jianfeng Lu +1
We study the problem of sampling from on , where is -strongly convex and -smooth, and write . We desi…
Exact simulation of diffusions and improved algorithms for log-concave sampling
Fan Chen, Sinho Chewi, Alexander Rakhlin +1
We study exact simulation of diffusions via rejection sampling on path space using unbiased estimators of the density ratio obtained from Girsanov's theorem. When applied to the un…
Algorithmic warm starts for Hamiltonian Monte Carlo
Matthew S. Zhang, Jason M. Altschuler, Sinho Chewi
Generating samples from a continuous probability density is a central algorithmic problem across statistics, engineering, and the sciences. For high-dimensional settings, Hamiltoni…
Sharp propagation of chaos in Rényi divergence
Matthew S. Zhang
We establish sharp rates for propagation of chaos in Rényi divergences for interacting diffusion systems at stationarity. Building upon the entropic hierarchy established in Lacker…
Sublinear iterations can suffice even for DDPMs
Matthew S. Zhang, Stephen Huan, Jerry Huang +3
SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been fo…
Stability of the Kim--Milman flow map
Sinho Chewi, Aram-Alexandre Pooladian, Matthew S. Zhang
In this short note, we characterize stability of the Kim--Milman flow map -- also known as the probability flow ODE -- with respect to variations in the target measure in relative…
Perspectives on Stochastic Localization
Bobby Shi, Kevin Tian, Matthew S. Zhang
We survey different perspectives on the stochastic localization process of Eldan, a powerful construction that has had many exciting recent applications in high-dimensional probabi…
Graph Random Features for Scalable Gaussian Processes
Matthew Zhang, Jihao Andreas Lin, Krzysztof Choromanski +3
We study the application of graph random features (GRFs) - a recently introduced stochastic estimator of graph node kernels - to scalable Gaussian processes on discrete input space…
Analysis of Langevin midpoint methods using an anticipative Girsanov theorem
Matthew S. Zhang
We introduce a new method for analyzing midpoint discretizations of stochastic differential equations (SDEs), which are frequently used in Markov chain Monte Carlo (MCMC) methods f…
Shifted Composition IV: Toward Ballistic Acceleration for Log-Concave Sampling
Jason M. Altschuler, Sinho Chewi, Matthew S. Zhang
Acceleration is a celebrated cornerstone of convex optimization, enabling gradient-based algorithms to converge sublinearly in the condition number. A major open question is whethe…
Uniform-in- log-Sobolev inequality for the mean-field Langevin dynamics with convex energy
Sinho Chewi, Atsushi Nitanda, Matthew S. Zhang
We establish a log-Sobolev inequality for the stationary distribution of mean-field Langevin dynamics with a constant that is independent of the number of particles . Our proof…