相关论文: Bayesian Posterior Sampling via Stochastic Gradien…

We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth…

Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…

In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily…

Recent work has argued that stochastic gradient descent can approximate the Bayesian uncertainty in model parameters near local minima. In this work we develop a similar correspondence for minibatch natural gradient descent (NGD). We prove…

This paper considers the use of a simple posterior sampling algorithm to balance between exploration and exploitation when learning to optimize actions such as in multi-armed bandit problems. The algorithm, also known as Thompson Sampling,…

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…

The generalized linear mixed model (GLMM) is widely used for analyzing correlated data, particularly in large-scale biomedical and social science applications. Scalable Bayesian inference for GLMMs is challenging because the marginal…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally expensive. Both the calculation of the acceptance probability and the creation of informed proposals usually require an iteration through the…

This paper introduces score-based sequential Langevin sampling (SSLS), a novel approach to nonlinear data assimilation within a recursive Bayesian filtering framework. The proposed method decomposes the assimilation process into alternating…

Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…

We propose Decentralized Proximal Stochastic Gradient Langevin Dynamics (DE-PSGLD), a decentralized Markov chain Monte Carlo (MCMC) algorithm for sampling from a log-concave probability distribution constrained to a convex domain.…

Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…

Scalable algorithms of posterior approximation allow Bayesian nonparametrics such as Dirichlet process mixture to scale up to larger dataset at fractional cost. Recent algorithms, notably the stochastic variational inference performs local…

Stochastic gradient MCMC methods, such as stochastic gradient Langevin dynamics (SGLD), employ fast but noisy gradient estimates to enable large-scale posterior sampling. Although we can easily extend SGLD to distributed settings, it…

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

A systematic procedure for optimising the friction coefficient in underdamped Langevin dynamics as a sampling tool is given by taking the gradient of the associated asymptotic variance with respect to friction. We give an expression for…