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ABSTRACT  

Te explosive growth in data volume and the availability of cheap computing resources have sparked
increasing interest in Big learning, an emerging subfeld that studies scalable machine learning algorithms,
systems and applications with Big Data. Bayesian methods represent one important class of statistical
methods for machine learning, with substantial recent developments on adaptive, flexible and scalable
Bayesian learning. Tis article provides a survey of the recent advances in Big learning with Bayesian
methods, termed Big Bayesian Learning, including non-parametric Bayesian methods for adaptively
inferring model complexity, regularized Bayesian inference for improving the flexibility via posterior
regularization, and scalable algorithms and systems based on stochastic subsampling and distributed
computing for dealing with large-scale applications. We also provide various new perspectives on the
large-scale Bayesian modeling and inference.