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Stochastic Expectation Maximization with Variance Reduction
Jianfei Chen · Jun Zhu · Yee Whye Teh · Tong Zhang

Wed Dec 05 02:00 PM -- 04:00 PM (PST) @ Room 210 #16

Expectation-Maximization (EM) is a popular tool for learning latent variable models, but the vanilla batch EM does not scale to large data sets because the whole data set is needed at every E-step. Stochastic Expectation Maximization (sEM) reduces the cost of E-step by stochastic approximation. However, sEM has a slower asymptotic convergence rate than batch EM, and requires a decreasing sequence of step sizes, which is difficult to tune. In this paper, we propose a variance reduced stochastic EM (sEM-vr) algorithm inspired by variance reduced stochastic gradient descent algorithms. We show that sEM-vr has the same exponential asymptotic convergence rate as batch EM. Moreover, sEM-vr only requires a constant step size to achieve this rate, which alleviates the burden of parameter tuning. We compare sEM-vr with batch EM, sEM and other algorithms on Gaussian mixture models and probabilistic latent semantic analysis, and sEM-vr converges significantly faster than these baselines.

Author Information

Jianfei Chen (RealAI)
Jun Zhu (Tsinghua University)
Yee Whye Teh (University of Oxford, DeepMind)

I am a Professor of Statistical Machine Learning at the Department of Statistics, University of Oxford and a Research Scientist at DeepMind. I am also an Alan Turing Institute Fellow and a European Research Council Consolidator Fellow. I obtained my Ph.D. at the University of Toronto (working with Geoffrey Hinton), and did postdoctoral work at the University of California at Berkeley (with Michael Jordan) and National University of Singapore (as Lee Kuan Yew Postdoctoral Fellow). I was a Lecturer then a Reader at the Gatsby Computational Neuroscience Unit, UCL, and a tutorial fellow at University College Oxford, prior to my current appointment. I am interested in the statistical and computational foundations of intelligence, and works on scalable machine learning, probabilistic models, Bayesian nonparametrics and deep learning. I was programme co-chair of ICML 2017 and AISTATS 2010.

Tong Zhang

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