Approximating Posterior Distributions in Belief Networks Using Mixtures

By Charles M. Bishop, Neil D. Lawrence, Tommi S. Jaakkola, Michael I. Jordan. 1997

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Variational Inference: A Review for Statisticians (2016, background): “Another way to expand the family is to consider mixtures of variational densities, that is, additional latent variables within the variational family (Bishop et al. 1998).”
The Variational Gaussian Process (2015, background): “Specifically, we recover the discrete mixture of mean-field distributions (Bishop et al., 1998; Jaakkola & Jordan, 1998).”
An Auxiliary Variational Method (2004, methodology): “Formally, (10) generalizes the term in the objective criterion ~ I ( x ; y ) ‚ log ~ q ( x j y ) q ( y ) q ( x ;y ) used by all the (known to us) variational mixture approaches (Jaakkola and Jordan (1998); Bishop et al. (1998); Lawrence et al. (1998); El-Hay and Friedman (2002)).”
Learning Bayesian networks: approaches and issues (2011, methodology): “authors have recently started to use variational methods to approximate the model and then use exact inference (Bishop et al., 1998; Jaakkola & Jordan, 1999a, 1999b; Jordan et al., 1999).”
Tractable Variational Structures for Approximating Graphical Models (1998, methodology): “Recently, variational ap proximations have been popular [2, 3, 4, 5], and have the advantage of providing rigorous bounds on quantities of interest, such as the data likelihood, in contrast to other approximate procedures such as Monte Carlo methods[l].”
Semi-Implicit Variational Inference (2018, methodology): “Examples include adding dependencies between latent variables (Saul & Jordan, 1996; Hoffman & Blei, 2015), using a mixture of variational distributions (Bishop et al., 1998; Gershman et al., 2012; Salimans & Knowles, 2013; Guo et al., 2016; Miller et al., 2017), introducing a copula to capture the d”
Affine Independent Variational Inference (2012, background): “Whilst mixtures of Gaussians [4, 10, 5] have previously been developed, these typically require additional bounds.”
Ensemble learning in Bayesian neural networks (1998, methodology): “This approach has already been applied successfully to the use of mixture distributions in variational treatments of sigmoidal belief networks ( Bishop, Lawrence, Jaakkola, and Jordan 1998 ) and Boltzmann machines (Lawrence, Bishop, and Jordan 1998).”
Boosting Variational Inference (2016, background): “…where φ = ( φ 1 , · · · , φ k ) is the collection of all component-wise parameters. single-component H 1 , namely a single-component While some authors [Bishop et al., 1998, Jaakkola and Jordan, 1998, Gershman et al., 2012] have considered H k for k > 1, these past works have focused on…”
Improving the Mean Field Approximation Via the Use of Mixture Distributions (1999, methodology): “Bishop, et al. (1997) have presented empirical results using the mixture approximation.”
Nonparametric variational inference (2012, methodology): “While mixture approximations have been studied in the variational inference literature (Bishop et al., 1998; Jaakola & Jordan, 1998), we develop this idea into a more generally applicable framework.”