The variational Bayesian EM algorithm for incomplete data: with application to scoring graphical model structures

By Matthew J. Beal, Zoubin Ghahramani. 2003

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Citations in the corpus

Variational Inference: A Review for Statisticians (2016, neutral): “This has been explored for mixture models (Ueda and Ghahramani 2002; McGrory and Titterington 2007) and more generally (Beal and Ghahramani 2003).”
Concrete Dropout (2017, methodology): “The output precision parameter τ was determined using a variational (MAP-)EM algorithm [3]: the variational parameters (variational E–step), and τ (M–step) are optimised iteratively by gradient ascent on (ELBO + log p ( τ )) .”
Fixed-Form Variational Posterior Approximation through Stochastic Linear Regression (2012, methodology): “…exponential form, choosing Q to be the set of factorized distributions q ( x ) = q ( x 1 ) q ( x 2 ) . . . q ( x k ) often leads to a tractable optimization problem that can be solved eﬃciently using an algorithm called Variational Bayes Expectation Maximization (VBEM, Beal and Ghahramani, 2002).”
Structured Priors for Structure Learning (2006, methodology): “Such data could be incorporated via approximations to the marginal likelihood such as those from [Beal and Ghahramani, 2003].”
MOrdReD: Memory-based Ordinal Regression Deep Neural Networks for Time Series Forecasting (2018, methodology): “We refer the reader to [42], [43], [44] and [45] for a more detailed discussion of Variational Bayes GMMs.”
Hierarchical Models in the Brain (2008, methodology): “This is known as variational Bayes; see [16] for an excellent treatment of static conjugate-exponential models.”
Mixed Membership Stochastic Blockmodels (2007, unknown): “The approximate variant of EM we describe here is often referred to as Variational EM (Beal and Ghahramani, 2003).”
Improving Inference for Neural Image Compression (2020, methodology): “We emphasize a distinction between variational inference and variational expectation maximization (EM) [Beal and Ghahramani, 2003]: whereas variational EM trains a model, VI is used to compress data using a trained model.”
Online Sparse Multi-Output Gaussian Process Regression and Learning (2019, methodology): “With particle resampling (line 8 in Algorithm 2), the ELBO is indeed used in a similar way as in [61] for selecting the particles, or equivalently speaking, choosing different sparse multi-output GP models.”
Advanced Lectures on Machine Learning (2004, methodology): “This approach can, for example, be used to score graphical model structures [54].”
A physics-aware, probabilistic machine learning framework for coarse-graining high-dimensional systems in the Small Data regime (2019, background): “if θk is effectively one of the component variables θ̃c,jm, τc,m, γjm, τcf,i,λ (n) c ), then the optimal Qθk(θk) can be found by setting the first order variation of F(Q) to zero yielding (Beal and Ghahramani, 2003)”
Unsupervised Learning (2018, unknown): “This approach can, for example, be used to score graphical model structures [54].”
DEM: A variational treatment of dynamic systems (2008, unknown): “This is known as variational Bayes; see Beal and Ghahramani (2003) for an excellent treatment of conjugate-exponential models.”
An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem (2007, methodology): “We do not address the alternative variational technique of forming a factorial approximation that minimizes a free-energy-based cost function [1], [2].”
Variational EM Algorithms for Non-Gaussian Latent Variable Models (2005, methodology): “In the ensemble learning approach (also Variational Bayes [4, 3, 6]) the idea is to ﬁnd the approximate separable posterior that minimizes the KL divergence from the true posterior, using the following decomposition of the log likelihood, log p ( y ) = q ( z | y ) log p ( z , y ) q ( z | y ) d z + D”