A family of algorithms for approximate Bayesian inference

By Tom Minka. 2001

394 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models (2022, background): “For instance, the original EP (Minka, 2001) considers Gaussian mixture likelihood (or Bernoulli likelihood for classification) and the moments can be directed obtained by the properties of Gaussian (or integration by parts).”
Effective Bayesian Modeling of Groups of Related Count Time Series (2014, methodology): “hich is a sequential projection approach, as well as numerical integration schemes such as the piecewise approximation of Kitagawa (1987). More recently, the expectation propagation (EP) algorithm of Minka (2001), a generalization of ADF, has proved successful in a number of non-linear ﬁltering and ”
Lightweight Probabilistic Deep Networks (2018, methodology): “1) of the intermediate layers, we rely on a form of expectation propagation (EP) [39].”
Assumed Density Filtering Methods for Learning Bayesian Neural Networks (2016, methodology): “Following (Hern´andez-Lobato and Adams 2015), we incorporate the prior terms N ( w ijl | 0 , λ − 1 ) into the approximate posterior using expectation propagation (EP) (Minka 2001a).”
Hierarchical Variational Models (2015, background): “The derivation of these two bounds parallels the development of expectation propagation (Minka, 2001) and variational Bayes (Jordan, 1999) which are based on alternative forms of the KL-divergence 4 .”
Stochastic Back-propagation and Variational Inference in Deep Latent Gaussian Models (2014, methodology): “Alternative variational algorithms such as expectation propagation (EP) (Minka, 2001) can also be used, but are numerically diﬃcult to implement and have performance similar to approaches based on the variational lower bound.”
Matchbox: large scale online bayesian recommendations (2009, positive): “This corresponds to the Sum-Product algorithm (for exact messages) and Expectation Propagation (for approximate messages) [10, 16].”
Distributed Bayesian Learning with Stochastic Natural Gradient Expectation Propagation and the Posterior Server (2015, methodology): “To start with, we may trivially formulate the target posterior distribution as an extended exponential family distribution with sufficient statistics s̃(x) := [s(x), `1(x), . . . , `n(x)] and natural parameters θ̃ := [θ0,1n] where 1n is a vector of 1’s of length n: p̃(x) = exp ( θ̃>s̃(x)− Ã(θ̃) ) .”
Automatic prediction of frustration (2007, methodology): “Examples of kernels include Gaussian functions, polynomial functions, etc.”
A Practical and Conceptual Framework for Learning in Control (2010, methodology): “The moment-matching approximation employed is equivalent to a unimodal approximation using Expectation Propagation (Minka, 2001).”
PAC-Bayesian Generalisation Error Bounds for Gaussian Process Classification (2003, neutral): “The experiments presented in Section 4 are based on the GPC methods we describe here.”
Bayesian pattern ranking for move prediction in the game of Go (2006, methodology): “This approach is a form of assumed-density (cid:12)ltering (Minka, 2001).”
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (2009, neutral): “Another approximation scheme that is popular in machine learning is the expectation–propagation (EP) approach (Minka, 2001); see for example Zoeter et al. (2005) and Kuss and Rasmussen (2005) for applications of EP to latent Gaussian models.”
Variational Bayesian Multinomial Probit Regression with Gaussian Process Priors (2006, methodology): “We will also show that the accuracy of this approximation is comparable to that obtained via MCMC. Thefollowing section introduces the multinomial-probit regression model with GP priors.”
Gaussian Processes for Object Categorization (2010, methodology): “Instead, one has to rely on numerical methods, such as MCMC (Williams and Barber 1998), or approximations of the posterior, e.g. Laplace and Expectation Propagation (Minka 2001).”
Expectation Propagation as a Way of Life: A Framework for Bayesian Inference on Partitioned Data (2014, methodology): “As discussed before in Section 2, if the approximating distribution forms an exponential family, minimizing the divergence conveniently corresponds to matching the moments of two distributions (Minka, 2001b).”