A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants

By Radford M. Neal, Geoffrey E. Hinton. 1998

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In Optimization & Training

Citations in the corpus

Density estimation using Real NVP (2016, background): “Recent advances in stochastic variational inference [22] and amortized inference [11, 36, 28, 42], allowed efﬁcient approximate inference and learning of deep directed graphical models by maximizing a variational lower bound on the log-likelihood [38].”
Gradient Estimation Using Stochastic Computation Graphs (2015, background): “Two broad categories of these problems are (1) likelihood maximization in probabilistic models with latent variables [17, 18], and (2) policy gradients in reinforcement learning [5, 23, 26].”
Learning Generative Visual Models from Few Training Examples: An Incremental Bayesian Approach Tested on 101 Object Categories (2004, methodology): “We now give an incremental version of the update rules, based on Neal and Hinton’s adaptation of conventional EM [16].”
Stochastic variational inference (2012, methodology): “In parallel, the mean-ﬁeld methods explained in Neal and Hinton (1999) (originally published in 1993) and Hinton and Van Camp (1993) led to variational algorithms for mixtures of experts (Waterhouse et al., 1996).”
Variational Inference: A Review for Statisticians (2016, background): “Neal and Hinton (1998, first published in 1993) made important connections to the expectation maximization (EM) algorithm (Dempster, Laird, and Rubin 1977), which then led to a variety of variational inference algorithms for other types of models (Waterhouse, MacKay, and Robinson 1996; MacKay 1997;…”
A Comprehensive guide to Bayesian Convolutional Neural Network with Variational Inference (2019, background): “This derivation forms an optimisation problem with a resulting cost function widely known as variational free energy [50, 63, 12] which is built upon two terms: the former, KL [qθ(w|D)‖p(w)], is dependent on the definition of the prior p(w), thus called complexity cost, whereas the latter, Eq(w|θ)[l”
Weight Uncertainty in Neural Networks (2015, background): “…on the weights: = arg min θ q ( w | θ ) log q ( w | θ ) P ( w ) P ( D| w ) d w The resulting cost function is variously known as the variational free energy (Neal and Hinton, 1998; Yedidia et al., 2000; Friston et al., 2007) or the expected lower bound (Saul et al., 1996; Neal and Hinton, 1998;…”
Distributed GraphLab: A Framework for Machine Learning in the Cloud (2012, background): “, belief propagation [13], expectation maximization [28], and stochastic optimization [35, 34]) where asynchronous procedures have been empirically shown to significantly outperform synchronous procedures.”
Sum-product networks: A new deep architecture (2011, background): “SPNs can also be learned using EM [17] by viewing sum nodes as implicit hidden variables, as described above.”
Large-Scale Feature Learning With Spike-and-Slab Sparse Coding (2012, background): “It works by maximizing a variational lower bound on the loglikelihood called the energy functional (Neal and Hinton, 1999).”
Mixture Models for Diverse Machine Translation: Tricks of the Trade (2019, methodology): “…current parameters θ ; M-step: update θ through each expert with gradients ∇ θ log p ( y ( i ) , z | x ( i ) ; θ ) weighted by their responsibilities r There are several ways to apply the E and M steps across training examples (Neal & Hinton, 1998); § 3.3 will review those considered in this work.”
Iterative Amortized Inference (2018, methodology): “Variational inference reformulates inference as optimization (Neal & Hinton, 1998; Hoffman et al., 2013).”
Noisy Natural Gradient as Variational Inference (2017, background): “Variational inference was ﬁrst applied to neural networks by Peterson (1987) and Hinton & Van Camp (1993).”
V-MPO: On-Policy Maximum a Posteriori Policy Optimization for Discrete and Continuous Control (2019, background): “…Policy improvement in V-MPO consists of the following two steps which have direct correspondences to the expectation maximization (EM) algorithm (Neal & Hinton, 1998): In the expectation (E) step, we choose the variational distribution ψ ( s, a ) such that the lower bound on log p θ ( I = 1) is…”
Multiband audio modeling for single-channel acoustic source separation (2004, background): “(5) with respect to theQ(S) factors[6], which are now called variational parameters.”