Stochastic zeroth-order discretizations of Langevin diffusions for Bayesian inference

DOI10.3150/21-BEJ1400MaRDI QIDQ2137043

Krishnakumar Balasubramanian, Saeed Ghadimi, Lingqing Shen, Abhishek Roy

Publication date: 16 May 2022

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.01373

zbMATH Keywords

Monte Carlo samplingBayesian inferenceLangevin diffusionderivative-free or zeroth-order samplingstochastic MCMC

Mathematics Subject Classification ID

Bayesian inference (62F15) Mathematical programming (90Cxx) Probabilistic methods, stochastic differential equations (65Cxx)

Uses Software

• ADVI

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The pseudo-marginal approach for efficient Monte Carlo computations
• Exponential convergence of Langevin distributions and their discrete approximations
• Accelerated randomized stochastic optimization.
• Sampling from a log-concave distribution with projected Langevin Monte Carlo
• Isoperimetric problems for convex bodies and a localization lemma
• Rates of convergence of the Hastings and Metropolis algorithms
• Langevin-type models. I: Diffusions with given stationary distributions and their discretizations
• Langevin-type models II: Self-targeting candidates for MCMC algorithms
• Improved regret for zeroth-order adversarial bandit convex optimisation
• Complexity of randomized algorithms for underdamped Langevin dynamics
• On sampling from a log-concave density using kinetic Langevin diffusions
• User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
• High-dimensional Bayesian inference via the unadjusted Langevin algorithm
• Couplings and quantitative contraction rates for Langevin dynamics
• On the efficiency of pseudo-marginal random walk Metropolis algorithms
• Spike and slab variable selection: frequentist and Bayesian strategies
• Stochastic online optimization. Single-point and multi-point non-linear multi-armed bandits. Convex and strongly-convex case
• Random gradient-free minimization of convex functions
• Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
• A companion for the Kiefer-Wolfowitz-Blum stochastic approximation algorithm
• Zeroth-order nonconvex stochastic optimization: handling constraints, high dimensionality, and saddle points
• Optimal Rates for Zero-Order Convex Optimization: The Power of Two Function Evaluations
• The geometry of logconcave functions and sampling algorithms
• Evaluating Derivatives
• Introduction to Derivative-Free Optimization
• Optimal Scaling of Discrete Approximations to Langevin Diffusions
• Introduction to Stochastic Search and Optimization
• Derivative-Free and Blackbox Optimization
• Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods
• Analysis and Geometry of Markov Diffusion Operators
• Kernel-based methods for bandit convex optimization
• The Hastings algorithm at fifty
• Derivative-free optimization methods
• Hit-and-Run Algorithms for Generating Multivariate Distributions
• Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming
• Theoretical Guarantees for Approximate Sampling from Smooth and Log-Concave Densities
• Stochastic Estimation of the Maximum of a Regression Function
• Multidimensional Stochastic Approximation Methods