A Variational Bayesian Framework for Graphical Models

By Hagai Thomas Attias. 1999

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Citations in the corpus

Fixed-Form Variational Posterior Approximation through Stochastic Linear Regression (2012, methodology): “A popular method of obtaining such an approximation is structured or fixed-form Variational Bayes, which works by numerically minimizing the Kullback-Leibler divergence of an approximating distribution in the exponential family to the intractable target distribution (Attias 2000; Beal and Ghahramani”
Variational inference for Dirichlet process mixtures (2006, methodology): “Thus far, variational methods have mainly been explored in the parametric setting, in particular within the formalism of the exponential family (Attias 2000; Ghahramani and Beal 2001; Blei et al. 2003).”
Expectation-Propogation for the Generative Aspect Model (2002, background): “(2001), which is a special case of “variational Bayes” (Attias, 2000), and Expectation-Propagation.”
A Stochastic Variational Framework for Fitting and Diagnosing Generalized Linear Mixed Models (2012, background): “el criticism. Keywords: Hierarchical model; Identify divergent units; Large longitudinal data; Non-conjugate model; Stochastic approximation; Variational Bayes 1. Introduction Variational Bayes (VB) (Attias, 2000) computational methods are very attractive for Bayesian inference with large data sets.”
Bayesian fMRI data analysis with sparse spatial basis function priors (2007, methodology): “The equations we obtain here are similar to those presented in (Attias, 2000; Penny, 2001) for a Gaussian mixture model with zero mean components.”
Non-conjugate Variational Message Passing for Multinomial and Binary Regression (2011, background): “It can be shown [1] that if the functions qi(xi) are unconstrained then minimising this functional can be achieved by coordinate descent, setting qi(xi) = exp〈log p(x)〉¬qi(xi), iteratively for each i, where 〈.”
A Bayesian approach for place recognition (2012, background): “These rules are omitted here for brevity but can be found in [30].”
Laplace Variational Approximation for Semiparametric Regression in the Presence of Heteroskedastic Errors (2016, methodology): “mixtures (Attias 2000), linear mixed models (Ormerod and Wand 2010), and nonparametric regression with missing data (Faes, Ormerod, and Wand 2011).”
Learning Latent Block Structure in Weighted Networks (2014, methodology): “ties by learning the parameters z;. Any of a large number of standard approaches can be used to optimize the likelihood function for the WSBM. Here, we describe an ecient variational Bayes approach [5], which eectively handles one technical diculty in tting the model to real data. Specically, learni”
A Tutorial on Bayesian Nonparametric Models (2011, methodology): “) We can use approximate methods, such as Markov chain Monte Carlo (McLachlan & Peel, 2000) or variational inference (Attias, 2000); thesemethods are discussed further in Section 4.”
Variational Bayesian Grammar Induction for Natural Language (2006, unknown): “The variational Bayes (VB) [1, 6] has succeeded in many applications [12, 17].”
Variational Bayesian inference for fMRI time series (2003, background): “The Bayesian Information Criterion (BIC) model order criterion has been shown to be a special case of the VB criterion (F), recovered in the limit of a large number of data points (Attias, 2000).”
Propagation Algorithms for Variational Bayesian Learning (2000, methodology): “Like for PCA [3], independent components analysis [1], and mixtures of factor analysers [5], the variational Bayesian algorithm for state-space models can be used to learn the structure of the model as well as average over parameters.”
Variational Message Passing (2005, methodology): “It has been noted (Attias, 2000; Ghahramani and Beal, 2001) that important simplifications to the variational update equations occur when the distributions of variables, condi-”
Bayesian analysis of neuroimaging data in FSL (2009, background): “Minimising the difference between the true and approximate distributions results in tractable integrals when there are conjugate priors (Attias, 2000; Penny et al., 2003).”