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Efficient Variational Inference for Hierarchical Models of Images, Text, and Networks
Variational inference provides a general optimization framework to approximate the posterior distributions of latent variables in probabilistic models. Although effective in simple scenarios, variational inference may be inaccurate or infeasible when the data is high-dimensional, the model structure is complicated, or variable relationships are non-conjugate. We propose solutions to these problems through the smart design and leverage of model structures, the rigorous derivation of variational bounds, and the creation of flexible algorithms for various models with rich, non-conjugate dependencies.Concretely, we first design an interpretable generative model for natural images, in which the hundreds of thousands of pixels per image are split into small patches represented by Gaussian mixture models. Through structured variational inference, the evidence lower bound of this model automatically recovers the popular expected patch log-likelihood method for image processing. A nonparametric extension using hierarchical Dirichlet processes further enables self-similarities to be captured and image-specific clusters created during inference, boosting image denoising and inpainting accuracy.Then we move on to text data, and design hierarchical topic graphs that generalize the bipartite noisy-OR models previously used for medical diagnosis. We derive auxiliary bounds to overcome the non-conjugacy of noisy-OR conditionals, and use stochastic variational inference to efficiently train on datasets with hundreds of thousands of documents. We dramatically increase the algorithm speed through a constrained family of variational bounds, so that only the ancestors of the sparse observed tokens of each document need to be considered.Finally, we propose a general-purpose Monte Carlo variational inference strategy that is directly applicable to any model with discrete variables. Compared to REINFORCE-style stochastic gradient updates, our coordinate-ascent updates have lower variance and converge much faster. Compared to auxiliary-variable bounds crafted for each individual model, our algorithm is simpler to derive and may be easily integrated into probabilistic programming languages for broader use. By avoiding auxiliary variables, we also tighten likelihood bounds and increase robustness to local optima. Extensive experiments on real-world models of images, text, and networks illustrate these appealing advantages
Streaming, Distributed Variational Inference for Bayesian Nonparametrics
This paper presents a methodology for creating streaming, distributed
inference algorithms for Bayesian nonparametric (BNP) models. In the proposed
framework, processing nodes receive a sequence of data minibatches, compute a
variational posterior for each, and make asynchronous streaming updates to a
central model. In contrast to previous algorithms, the proposed framework is
truly streaming, distributed, asynchronous, learning-rate-free, and
truncation-free. The key challenge in developing the framework, arising from
the fact that BNP models do not impose an inherent ordering on their
components, is finding the correspondence between minibatch and central BNP
posterior components before performing each update. To address this, the paper
develops a combinatorial optimization problem over component correspondences,
and provides an efficient solution technique. The paper concludes with an
application of the methodology to the DP mixture model, with experimental
results demonstrating its practical scalability and performance.Comment: This paper was presented at NIPS 2015. Please use the following
BibTeX citation: @inproceedings{Campbell15_NIPS, Author = {Trevor Campbell
and Julian Straub and John W. {Fisher III} and Jonathan P. How}, Title =
{Streaming, Distributed Variational Inference for Bayesian Nonparametrics},
Booktitle = {Advances in Neural Information Processing Systems (NIPS)}, Year
= {2015}
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