97 citations · 296 across the 13 of their papers we have counts for
14 papers
Efficient Sampling on Riemannian Manifolds via Langevin MCMC
Xiang Cheng, Jingzhao Zhang, Suvrit Sra
We study the task of efficiently sampling from a Gibbs distribution over a Riemannian manifold via (geometric) Langevin MCMC; this algorithm involves…
Restart Sampling for Improving Generative Processes
Yilun Xu, Mingyang Deng, Xiang Cheng +3
Generative processes that involve solving differential equations, such as diffusion models, frequently necessitate balancing speed and quality. ODE-based samplers are fast but plat…
Fast Conditional Mixing of MCMC Algorithms for Non-log-concave Distributions
Xiang Cheng, Bohan Wang, Jingzhao Zhang +1
MCMC algorithms offer empirically efficient tools for sampling from a target distribution . However, on the theory side, MCMC algorithms suffer from slow…
Theory and Algorithms for Diffusion Processes on Riemannian Manifolds
Xiang Cheng, Jingzhao Zhang, Suvrit Sra
We study geometric stochastic differential equations (SDEs) and their approximations on Riemannian manifolds. In particular, we introduce a simple new construction of geometric SDE…
Convergence analysis of discrete high-index saddle dynamics
Yue Luo, Xiangcheng Zheng, Xiangle Cheng +1
Saddle dynamics is a time continuous dynamics to efficiently compute the any-index saddle points and construct the solution landscape. In practice, the saddle dynamics needs to be…
Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithm
Sinho Chewi, Chen Lu, Kwangjun Ahn +3
Conventional wisdom in the sampling literature, backed by a popular diffusion scaling limit, suggests that the mixing time of the Metropolis-Adjusted Langevin Algorithm (MALA) scal…
Stochastic Gradient and Langevin Processes
Xiang Cheng, Dong Yin, Peter L. Bartlett +1
We prove quantitative convergence rates at which discrete Langevin-like processes converge to the invariant distribution of a related stochastic differential equation. We study the…
Is There an Analog of Nesterov Acceleration for MCMC?
Yi-An Ma, Niladri Chatterji, Xiang Cheng +3
We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective fu…
Quantitative Weak Convergence for Discrete Stochastic Processes
Xiang Cheng, Peter L. Bartlett, Michael I. Jordan
In this paper, we quantitative convergence in for a family of Langevin-like stochastic processes that includes stochastic gradient descent and related gradient-based algorith…
Sharp convergence rates for Langevin dynamics in the nonconvex setting
Xiang Cheng, Niladri S. Chatterji, Yasin Abbasi-Yadkori +2
We study the problem of sampling from a distribution , where the function is -smooth everywhere and -strongly convex outside a ball…
Underdamped Langevin MCMC: A non-asymptotic analysis
Xiang Cheng, Niladri S. Chatterji, Peter L. Bartlett +1
We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show…
Convergence of Langevin MCMC in KL-divergence
Xiang Cheng, Peter Bartlett
Langevin diffusion is a commonly used tool for sampling from a given distribution. In this work, we establish that when the target density is such that is smoo…
FLAG n' FLARE: Fast Linearly-Coupled Adaptive Gradient Methods
Xiang Cheng, Farbod Roosta-Khorasani, Stefan Palombo +2
We consider first order gradient methods for effectively optimizing a composite objective in the form of a sum of smooth and, potentially, non-smooth functions. We present accelera…
Asymptotic behavior of -based Laplacian regularization in semi-supervised learning
Ahmed El Alaoui, Xiang Cheng, Aaditya Ramdas +2
Given a weighted graph with vertices, consider a real-valued regression problem in a semi-supervised setting, where one observes labeled vertices, and the task is to label…