High-Order Stochastic Gradient Thermostats for Bayesian Learning of Deep Models

Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of uncertainty in the model parameters. Stochastic gradient MCMC algorithms (SG-MCMC) are a family of diffusion-based sampling methods for large-scale Bayesian learning. In SG-MCMC, multivariate stochastic gradient thermostats (mSGNHT) augment each parameter of interest, with a momentum and a thermostat variable to maintain stationary distributions as target posterior distributions. As the number of variables in a continuous-time diffusion increases, its numerical approximation error becomes a practical bottleneck, so better use of a numerical integrator is desirable. To this end, we propose use of an efficient symmetric splitting integrator in mSGNHT, instead of the traditional Euler integrator. We demonstrate that the proposed scheme is more accurate, robust, and converges faster. These properties are demonstrated to be desirable in Bayesian deep learning. Extensive experiments on two canonical models and their deep extensions demonstrate that the proposed scheme improves general Bayesian posterior sampling, particularly for deep models.Comment: AAAI 201

Scaling up Dynamic Edge Partition Models via Stochastic Gradient MCMC

The edge partition model (EPM) is a generative model for extracting an overlapping community structure from static graph-structured data. In the EPM, the gamma process (GaP) prior is adopted to infer the appropriate number of latent communities, and each vertex is endowed with a gamma distributed positive memberships vector. Despite having many attractive properties, inference in the EPM is typically performed using Markov chain Monte Carlo (MCMC) methods that prevent it from being applied to massive network data. In this paper, we generalize the EPM to account for dynamic enviroment by representing each vertex with a positive memberships vector constructed using Dirichlet prior specification, and capturing the time-evolving behaviour of vertices via a Dirichlet Markov chain construction. A simple-to-implement Gibbs sampler is proposed to perform posterior computation using Negative- Binomial augmentation technique. For large network data, we propose a stochastic gradient Markov chain Monte Carlo (SG-MCMC) algorithm for scalable inference in the proposed model. The experimental results show that the novel methods achieve competitive performance in terms of link prediction, while being much faster

Dirichlet belief networks for topic structure learning

Recently, considerable research effort has been devoted to developing deep architectures for topic models to learn topic structures. Although several deep models have been proposed to learn better topic proportions of documents, how to leverage the benefits of deep structures for learning word distributions of topics has not yet been rigorously studied. Here we propose a new multi-layer generative process on word distributions of topics, where each layer consists of a set of topics and each topic is drawn from a mixture of the topics of the layer above. As the topics in all layers can be directly interpreted by words, the proposed model is able to discover interpretable topic hierarchies. As a self-contained module, our model can be flexibly adapted to different kinds of topic models to improve their modelling accuracy and interpretability. Extensive experiments on text corpora demonstrate the advantages of the proposed model.Comment: accepted in NIPS 201