The EP energy function and minimization schemes

By Tom Minka. 2001

46 citations recorded by the source corpus.

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In Mathematical Optimization

Citations in the corpus

Discriminative Embeddings of Latent Variable Models for Structured Data (2016, neutral): “C.2 Damped BP Instead of the primal form of Bethe free energy, Minka (2001) investigates the duality of the optimization, min γ max λ ∑ i ( |N (i)| − 1 ) log ∫ H Φ(hi, xi) exp(γi(hi))dhi − ∑ (i,j)∈E log ∫ H2 Ψ(hi, hj)Φ(hi, xi)Φ(hj , xj) exp(λij(hj) + λji(hi))dhjdhi, subject to ( |N (i)| − 1 )…”
Unsupervised Learning (2018, unknown): “Convergent forms of EP can be derived by making use of the EP energy function [70] although these may not be as fast and simple to implement as the algorithm in Figure 5.”
Power EP (2004, methodology): “Power EP was originally described by Minka & Lafferty (2002), briefly and without derivation. Later, Wiegerinck & Heskes (2002) discussed an algorithm called “fractional belief propagation”, describing its energy function and an interpretation in terms of α-divergence.”
Advanced Lectures on Machine Learning (2004, methodology): “Convergent forms of EP can be derived by making use of the EP energy function [70] although these may not be as fast and simple to implement as the algorithm in Figure 5.”
Bayesian Gaussian process models : PAC-Bayesian generalisation error bounds and sparse approximations (2003, methodology): “For EP applied to full GP models, such a criterion can be constructed by generalising the Bethe free energy [217] as an analogous criterion for (loopy) belief propagation (see [123]).”
Expectation propagation for approximate inference in dynamic Bayesian networks (2002, background): “The damped versions suggested in (Minka, 2001a) and (Murphy et al., 1999) for loopy belief propagation are slightly di erent and may not share this property.”
Divergence measures and message passing (2005, background): “As a function of the message parameters τ a, its stationary points are exactly the fixed points of α-divergence message passing (Minka, 2004; Minka, 2001a).”
Stable Fixed Points of Loopy Belief Propagation Are Local Minima of the Bethe Free Energy (2002, methodology): “We replace the bound (7) with an explicit minimization over auxiliary variables γ (see also [7]; an alternative interpretation is a Legendre transform): − ∑”