Power EP

By Tom Minka. 2004

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Citations in the corpus

Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling (2018, methodology): “We focus on methods that directly optimize the global EP objective via stochastic gradient descent, as, for instance, Power EP (Minka, 2004).”
Streaming Sparse Gaussian Process Approximations (2017, neutral): “(5) with a more general α-divergence [16].”
Black-box $\alpha$-divergence Minimization (2015, neutral): “5 / 13 Local α-divergence minimization (Power EP) Approximates p(θ) ∝ p0(θ) ∏N n=1 fn(θ) with q(θ) ∝ p0(θ) ∏N n=1 f̃n(θ) [Minka, 2004] The f̃n are tuned by minimizing the local α-divergences Dα[pn||q] for n = 1, . . . ,N , where pn(θ) ∝ fn(θ) ∏ j 6=n f̃j(θ) q(θ) ∝ f̃n(θ) ∏ j 6=n f̃j(θ) .”
Bayesian Inference and Optimal Design in the Sparse Linear Model (2007, methodology): “A way to circumvent this problem is to employ fractional EP updates (these have been introduced in a different context in [7]), which can be understood by imagining the site ti being replaced by q fractional replicas fi = t 1/q i .”
Distributed Bayesian Learning with Stochastic Natural Gradient Expectation Propagation and the Posterior Server (2015, methodology): “Typically, we take βi = 1 which corresponds to standard EP, while βi → ∞ corresponds to variational Bayes (Wiegerinck and Heskes, 2003, Minka, 2004).”
Pattern Recognition and Machine Learning (2006, unknown): “, 2005), fractional belief propagation (Wiegerinck and Heskes, 2003), and power EP (Minka, 2004).”
Advances in Variational Inference (2017, background): “Some recent extensions of EP [101], [125], [204], [228] can be viewed as classical EP with”
Divergence measures and message passing (2005, background): “The motivation for this is that some divergences may be easier to minimize for certain factors (Minka, 2004).”
Learning Feature Selection Dependencies in Multi-task Learning (2013, background): “Damping significantly improves the convergence of EP but leaves the fixed points of the algorithm invariant [22].”
MAP estimation via agreement on trees: message-passing and linear programming (2005, background): “the MAP optimal solution that the reweighted message-passing recovered was above 80% for all the examples that we considered; for mixed problems with weaker observation terms , this fraction can be lower (see [36]).”
Bayesian inference for Plackett-Luce ranking models (2009, methodology): “Message update for a P-L factor As a clari.cation to (Minka, 2005), and matching the original Power EP description in (Minka, 2004), the marginal updates and the message updates are: new q (vi)= qi(vi)2/qH(vi) (20) iinew q(vi) new i m = (21) a.i mi.a(vi) 3.4.”
A Unifying Framework for Sparse Gaussian Process Approximation using Power Expectation Propagation (2016, methodology): “…methods that can sidestep these intractabilities [4–19] This paper develops a general sparse approximate inference framework based upon Power Expectation Propagation (PEP) [20] that uniﬁes many of these approximations, extends them signiﬁcantly, and provides improvements in practical settings.”
Expectation Propagation as a Way of Life (2020, methodology): “Fractional EP (Minka, 2004) is an extension of EP which can be used to improve the robustness of the algorithm when the approximation family is not flexible enough (Minka, 2005) or when the propagation of information is difficult due to vague prior information (Seeger, 2008).”
Graphical Models, Exponential Families, and Variational Inference (2008, background): “With different motivations, not directly related to convexity and uniqueness, Minka [170] has discussed reweighted forms of EP, referred to as “power EP.”
Rényi Divergence Variational Inference (2016, background): “Both algorithms were originally proposed to approximate (power) EP [3, 26], which usually minimises α-divergences locally, and considers M = 1, α ∈ [1− 1/N, 1) and exponential family distributions.”
Stochastic Expectation Propagation (2015, background): “The same pathology exists for the broader class of power-EP (PEP) algorithms [12] that includes variational message-passing [13].”
Operator Variational Inference (2016, methodology): “Given a data set x , approximate Bayesian inference seeks to approximate the posterior distribution p. z j x / , which is applied in Variational inference posits a family of approximating distributions q. z / and E q. z / Œ log p. x ; z / log q. z /(cid:141):”
Approximate Gaussian Integration using Expectation Propagation (2011, methodology): “The Power-EP algorithm is an extension of EP where the factors are raised to a specific power αi before moment matching (Minka, 2004).”