An Auxiliary Variational Method

By Felix V. Agakov, David Barber. 2004

75 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Energy-Inspired Models: Learning with Sampler-Induced Distributions (2019, background): “R | Agakov and Barber [1], Salimans et al. [61], Ranganath et al. [57], Maaløe et al. [46] develop an auxiliary variable variational bound (1)), however, the density of the EIM q ( z x ) is intractable. where r ( | z, x ) is a variational distribution meant to model q ( | z, x ) , and the identity…”
Auxiliary Deep Generative Models (2016, methodology): “In this paper we propose a variational auxiliary variable approach (Agakov and Barber, 2004) to improve the variational distribution: The generative model is extended with variables a to p ( x, z, a ) such that the original model is invariant to marginalization over a : p ( x, z, a ) = p ( a | x, z…”
Multiplicative Normalizing Flows for Variational Bayesian Neural Networks (2017, methodology): “In Section 2 we will show how we can produce very ﬂexible distributions in an efﬁcient way by employing auxiliary random variables (Agakov & Barber, 2004; Salimans et al., 2013; Ranganath et al., 2015; Maaløe et al., 2016) and normalizing ﬂows (Rezende & Mohamed, 2015).”
The Variational Gaussian Process (2015, methodology): “We derive an algorithm for black box inference over a wide class of generative models.”
Hierarchical Variational Models (2015, background): “For undirected models Agakov and Barber (2004) introduced the auxiliary bound for variational inference we derive.”
Importance Weighting and Variational Inference (2018, background): “Thus, IWVI can be seen as an instance of auxiliary variational inference [1] where a joint divergence upper-bounds the divergence of interest.”
Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Models (2020, methodology): “This boils down to the hierarchical variational method (Agakov & Barber, 2004; Ranganath et al., 2016) as a special case when one step of autoencoding transform is applied.”
Multiple Causal Inference with Latent Confounding (2018, methodology): “We can use the entropy bounds with auxiliary distributions on the conditioning set, as used in variational inference [ 1, 33, 30, 23 ] .”
Importance Weighted Hierarchical Variational Inference (2019, methodology): “In the direction of improving the single-sample ELBO Agakov and Barber (2004); Salimans et al. (2015); Maaløe et al. (2016); Ranganath et al. (2016) proposed to use a hierarchical variational model (HVM) for qφ(z | x) = ∫ qφ(z | x, ψ)qφ(ψ | x)dψ with explicit joint density qφ(z, ψ | x), where ψ are ”
Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows (2019, background): “However, it may be possible to use CIFs in the context of an extended-space variational framework along the lines of Agakov & Barber (2004), and we leave this for future work.”
Improving Semi-Supervised Learning with Auxiliary Deep Generative Models (2015, methodology): “Further the stochasticity of a maps each input into a distribution q(a|x) used for the discriminative classifier, which is richer than a deterministic dependency between x and y (Agakov and Barber, 2004).”
Exploiting Hierarchy for Learning and Transfer in KL-regularized RL (2019, background): “This formulation also has interesting connections to auxiliary variable formulations in the approximate inference literature (Salimans et al., 2014; Agakov & Barber, 2004).”
Semi-Implicit Variational Inference (2018, methodology): “SIVI is related to the hierarchical variational model (Ran-ganath et al., 2016; Maaløe et al., 2016; Agakov & Barber, 2004) in using a hierarchical variational distribution, but, as discussed below, differs from it in allowing an implicit mixing distribution q φ ( ψ ) and optimizing the variational…”
Divide and Couple: Using Monte Carlo Variational Objectives for Posterior Approximation (2019, unknown): “bounds and auxiliary variational inference [1].”