Owing to the recent advances in "Big Data" modeling and prediction tasks, variational Bayesian estimation has gained popularity due to their ability to provide exact solutions to approximate posteriors. One key technique for approximate inference is stochastic variational inference (SVI). SVI poses variational inference as a stochastic optimization problem and solves it iteratively using noisy gradient estimates. It aims to handle massive data for predictive and classification tasks by applying complex Bayesian models that have observed as well as latent variables. This paper aims to decentralize it allowing parallel computation, secure learning and robustness benefits. We use Alternating Direction Method of Multipliers in a top-down setting to develop a distributed SVI algorithm such that independent learners running inference algorithms only require sharing the estimated model parameters instead of their private datasets. Our work extends the distributed SVI-ADMM algorithm that we first propose, to an ADMM-based networked SVI algorithm in which not only are the learners working distributively but they share information according to rules of a graph by which they form a network. This kind of work lies under the umbrella of deep learning over networks' and we verify our algorithm for a topic-modeling problem for corpus of Wikipedia articles. We illustrate the results on latent Dirichlet allocation (LDA) topic model in large document classification, compare performance with the centralized algorithm, and use numerical experiments to corroborate the analytical results.
None of these works use stochastic optimization methods to speed up inference and hence they are fundamentally different from standard SVI itself. One recent work Extended-SVI' by @cite_4 retains the benefits of SVI while making it distributed and asynchronous. They employ a rather simple algorithmic change to SVI however their work remains unexplored in terms of depth because they particularly focus on Gaussian mixture models and do not provide how it is extendable to all other probabilistic models for which SVI in general works.
@cite_4
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Stochastic variational inference (SVI), the state-of-the-art algorithm for scaling variational inference to large-datasets, is inherently serial. Moreover, it requires the parameters to fit in the memory of a single processor; this is problematic when the number of parameters is in billions. In this paper, we propose extreme stochastic variational inference (ESVI), an asynchronous and lock-free algorithm to perform variational inference for mixture models on massive real world datasets. ESVI overcomes the limitations of SVI by requiring that each processor only access a subset of the data and a subset of the parameters, thus providing data and model parallelism simultaneously. We demonstrate the effectiveness of ESVI by running Latent Dirichlet Allocation (LDA) on UMBC-3B, a dataset that has a vocabulary of 3 million and a token size of 3 billion. In our experiments, we found that ESVI not only outperforms VI and SVI in wallclock-time, but also achieves a better quality solution. In addition, we propose a strategy to speed up computation and save memory when fitting large number of topics.