arXiv research

Langevin MCMC samples efficiently from Riemannian manifolds with geometric Euler-Murayama analysis.

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 that it achieves $\varepsilon$ error (in 2-Wasserstein distance) in $\mathcal{O}(\sqrt{d}/\varepsilon)$ steps. This is a significant improv…

Langevin autoencoders improve deep latent variable models with efficient posterior sampling.

Recent works have derived non-asymptotic upper bounds for convergence of underdamped Langevin MCMC. We revisit these bound and consider introducing scaling terms in the underlying underdamped Langevin equation. In particular, we provide conditions under which an appropriate scaling allows to improve the error bounds in…

Optimal preconditioning improves Langevin sampling efficiency.

Stochastic EM with biased MCMC improves inference stability.

New Langevin method achieves third order convergence for strongly log-concave distributions.

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 functional. We show that an underdamped form of the Langevin algorithm performs accelerated gradient descent in this metric. To characterize t…

The paper provides privacy guarantees for MCMC algorithms using Langevin dynamics.

Proposes a new Langevin flow approach for VAEs.

Study Langevin Monte Carlo for sampling non-log-concave distributions.

We study the problem of sampling from a distribution $p^*(x) \propto \exp\left(-U(x)\right)$, where the function $U$ is $L$-smooth everywhere and $m$-strongly convex outside a ball of radius $R$, but potentially nonconvex inside this ball. We study both overdamped and underdamped Langevin MCMC and establish upper bound…

Two popular classes of methods for approximate inference are Markov chain Monte Carlo (MCMC) and variational inference. MCMC tends to be accurate if run for a long enough time, while variational inference tends to give better approximations at shorter time horizons. However, the amount of time needed for MCMC to exceed…

A new method learns latent space normalizing flow for approximate inference in generator models.

SGLDiff approximates Bayesian posterior distributions with subsampling error.

This work improves VAEs using MCMC methods for better variational bounds.

DE-PSGLD samples from constrained distributions in a decentralized manner.

Study improves sampling from complex distributions using annealed Langevin Monte Carlo.

A new Monte Carlo sampling method derived from reverse diffusion.

Adaptive-stepsize MCMC sampling inspired by Adam optimizer.

Analyzes learning and applying preconditioners in MCMC for efficiency.

This paper proposes a method to train energy-based models using variational auto-encoders for efficient sampling.

SGBD algorithm improves robustness in Bayesian sampling.

LMC-TS uses MCMC for efficient posterior sampling in contextual bandits.

New sampling method on Lie groups converges quickly.

It is known that the Langevin dynamics used in MCMC is the gradient flow of the KL divergence on the Wasserstein space, which helps convergence analysis and inspires recent particle-based variational inference methods (ParVIs). But no more MCMC dynamics is understood in this way. In this work, by developing novel conce…

STANLEY improves sampling for complex data models.

This paper studies the fundamental problem of learning deep generative models that consist of multiple layers of latent variables organized in top-down architectures. Such models have high expressivity and allow for learning hierarchical representations. Learning such a generative model requires inferring the latent va…

Paper proposes CoopFlow, a two-flow generator for energy-based models.

We propose a stochastic gradient Markov chain Monte Carlo (SG-MCMC) algorithm for scalable inference in mixed-membership stochastic blockmodels (MMSB). Our algorithm is based on the stochastic gradient Riemannian Langevin sampler and achieves both faster speed and higher accuracy at every iteration than the current sta…

This study investigates the effects of Markov chain Monte Carlo (MCMC) sampling in unsupervised Maximum Likelihood (ML) learning. Our attention is restricted to the family of unnormalized probability densities for which the negative log density (or energy function) is a ConvNet. We find that many of the techniques used…

A fast MCMC sampler for sparse Bayesian inference.

In this paper, we explore a general Aggregated Gradient Langevin Dynamics framework (AGLD) for the Markov Chain Monte Carlo (MCMC) sampling. We investigate the nonasymptotic convergence of AGLD with a unified analysis for different data accessing (e.g. random access, cyclic access and random reshuffle) and snapshot upd…

The paper explores efficient sampling for Bayesian wide neural networks.

New algorithms improve sampling from complex distributions.

Langevin diffusion is a commonly used tool for sampling from a given distribution. In this work, we establish that when the target density $p^*$ is such that $\log p^*$ is $L$ smooth and $m$ strongly convex, discrete Langevin diffusion produces a distribution $p$ with $KL(p||p^*)\leq ε$ in $\tilde{O}(\frac{d}ε)$ steps,…

Particle MCMC is a class of algorithms that can be used to analyse state-space models. They use MCMC moves to update the parameters of the models, and particle filters to propose values for the path of the state-space model. Currently the default is to use random walk Metropolis to update the parameter values. We show …

New Langevin algorithms improve sampling efficiency in high dimensions.

We propose a Markov chain Monte Carlo (MCMC) algorithm based on third-order Langevin dynamics for sampling from distributions with log-concave and smooth densities. The higher-order dynamics allow for more flexible discretization schemes, and we develop a specific method that combines splitting with more accurate integ…

Langevin Dynamics speeds up mixing time with manifold hypothesis and multi-scale approach.

As an important Markov Chain Monte Carlo (MCMC) method, stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. However, SGLD typically suffers from slow convergence rate due to its large variance caused by the stochastic gradient. In order to allev…

New analysis for learning and applying preconditioners in MCMC improves efficiency.

Theoretical proof shows COMs are a type of contrastive divergence model with improved sampling.

A new sampling method estimates scores without training or nested MCMC.

It is well-known that irreversible MCMC algorithms converge faster to their stationary distributions than reversible ones. Using the special geometric structure of Lie groups $\mathcal G$ and dissipation fields compatible with the symplectic structure, we construct an irreversible HMC-like MCMC algorithm on $\mathcal G…

Proves convergence of PSGLA for sampling non-convex potentials.

Thompson sampling for multi-armed bandit problems is known to enjoy favorable performance in both theory and practice. However, it suffers from a significant limitation computationally, arising from the need for samples from posterior distributions at every iteration. We propose two Markov Chain Monte Carlo (MCMC) meth…

Neural network MCMC sampler maximizes proposal entropy for efficient sampling.