Variational algorithms for approximate Bayesian inference

By Matthew J. Beal. 2003

2,078 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Neural Variational Inference for Text Processing (2015, background): “In order to have a tight lower bound, the variational distribution q ( h ) should approach the true posterior p ( h | x , y ) .”
Making Tree Ensembles Interpretable (2016, background): “The lower-bound of (5) is derived as∑N n=1 ∑K k=1 Eq(u)[u (n) k ] ( log q(z(n)|k)q(s(n)|k)q(k|x(n)) ) − ∑N n=1 ∑K k=1 Eq(u)[log q(u (n) k )], (6) where u(n)k ∈ {0, 1}, ∑K k=1 u (n) k = 1, and q(u) is an arbitrary distribution on u (Beal, 2003).”
Semi-analytical approximations to statistical moments of sigmoid and softmax mappings of normal variables (2017, background): “We also expose a few niche applications of these approximations, which mainly arise in the context of variational Bayesian inference (Beal, 2003; Daunizeau et al., 2009; Friston et al., 2007; Smídl and Quinn, 2006) on specific generative models.”
Stochastic Back-propagation and Variational Inference in Deep Latent Gaussian Models (2014, methodology): “A number of approaches are known and currently used, in particular algorithms based on mean-ﬁeld variational EM (Beal, 2003), the wake-sleep algorithm (Dayan, 2000), policy-gradient methods such as REINFORCE (Williams, 1992), or stochastic gradient methods (Hoﬀman et al., 2012).”
Automated Variational Inference in Probabilistic Programming (2013, background): “An unconditional probabilistic program f is deﬁned as a parameterless function with an arbitrary mix of deterministic and stochastic elements.”
Community detection in graphs (2009, methodology): “In a successive paper (Vazquez, 2008), Vázquez showed that better results are obtained if the classification likelihood is maximized by using Variational Bayes (Beal, 2003; Jordan et al., 1999).”
Variational inference for Dirichlet process mixtures (2006, background): “Further perspectives on algorithms of this kind can be found in Xing et al. (2003) and Beal (2003) .”
Coordinated Multi-Agent Imitation Learning (2017, methodology): “The structure learning LearnStructure and role assignment Assign components are based on graphi-Algorithm (Hoffman et al., 2013; Johnson & Willsky, 2014; Beal, 2003) on the same mini-batches.”
Continual Multi-task Gaussian Processes (2019, methodology): “Due to abrupt changes in the hyperparameters may affect the learning process of q ( u new | ψ new ) , which is sensitive to amplitude or smoothness, we use several steps of the variational EM algorithm (Beal, 2003) within each sequential update.”
A Multitask Point Process Predictive Model (2015, methodology): “Choosing a linear kernel for (2) and (3) (KNN,ij = hTi hj), and letting v = g = 0, the construction through (2)-(3) is equivalent to the multitask linear regression model in (6)-(8) on a finite observed dataset.”
Bayesian HMM clustering of x-vector sequences (VBx) in speaker diarization: theory, implementation and analysis on standard tasks (2020, methodology): “For the Bayesian HMM, the ELBO can be efficiently evaluated (see page 95 of [25]) as”
Variational Inference for the Indian Buffet Process (2009, methodology): “Mean field variational methods approximate the true posterior with a variational distribution qΦ(W ) from some tractable family of distributions Q (Beal, 2003; Wainwright and Jordan, 2008).”
Understanding the origin of information-seeking exploration in probabilistic objectives for control (2021, background): “Moreover, we show that how both our abstract classes of Evidence and Divergence objectives relate to currently known objectives such as the ELBO (Beal, 2003), control-as-inference (Kappen, 2007; K. C. Rawlik, 2013), the expected free energy in active inference (K. Friston et al., 2015a), action and ”
Bayesian Intermittent Demand Forecasting for Large Inventories (2016, methodology): “We employ approximate Bayesian inference in a linear dynamical system, for which there is a lot of prior work in Machine Learning [3, 1, 2].”
VBA: A Probabilistic Treatment of Nonlinear Models for Neurobiological and Behavioural Data (2014, positive): “which is finessed using variational approaches that rest on optimizing a free-energy lower bound F q ð Þ to the model evidence, with respect to an approximate conditional density q q ð Þ [8]:”