Adversarial Message Passing For Graphical Models

By Theofanis Karaletsos. 2016

29 citations recorded by the source corpus.

Bayesian inference on structured models typically relies on the ability to infer posterior distributions of underlying hidden variables. However, inference in implicit models or complex posterior distributions is hard. A popular tool for learning implicit models are generative adversarial networks (GANs) which learn parameters of generators by fooling discriminators. Typically, GANs are considered to be models themselves and are not understood in the context of inference. Current techniques rely on inefficient global discrimination of joint distributions to perform learning, or only consider discriminating a single output variable. We overcome these limitations by treating GANs as a basis for likelihood-free inference in generative models and generalize them to Bayesian posterior inference over factor graphs. We propose local learning rules based on message passing minimizing a global divergence criterion involving cooperating local adversaries used to sidestep explicit likelihood evaluations. This allows us to compose models and yields a unified inference and learning framework for adversarial learning. Our framework treats model specification and inference separately and facilitates richly structured models within the family of Directed Acyclic Graphs, including components such as intractable likelihoods, non-differentiable models, simulators and generally cumbersome models. A key result of our treatment is the insight that Bayesian inference on structured models can be performed only with sampling and discrimination when using nonparametric variational families, without access to explicit distributions. As a side-result, we discuss the link to likelihood maximization. These approaches hold promise to be useful in the toolbox of probabilistic modelers and enrich the gamut of current probabilistic programming applications.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Graph Learning, Probabilistic & Bayesian Methods

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Citations in the corpus

Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks (2017, background): “A similar idea was also mentioned by Karaletsos (2016) in the context of message passing in graphical models.”
Learning in Implicit Generative Models (2016, methodology): “For example, Karaletsos (2016) use GAN-like techniques for inference in factor graphs, and since the central quantity of variational inference is a density ratio it is possible to propose a modiﬁed variational inference using implicit models, as discussed by Mescheder et al. (2017) and Huszár…”
Variational Approaches for Auto-Encoding Generative Adversarial Networks (2017, background): “This trick is widespread [16, 18, 24, 25, 37], although perhaps not stated as explicitly.”
Deep and Hierarchical Implicit Models (2017, background): “In this section we describe the idea of implicit densities and develop two new classes of models: hierarchical implicit models and deep implicit models.”
Hierarchical Implicit Models and Likelihood-Free Variational Inference (2017, background): “Implicit-like variational approximations have also appeared in auto-encoder frameworks [32, 34] and message passing [24].”
Gradient Estimators for Implicit Models (2017, background): “Very recently, implicit distributions have also been considered as approximate posterior distributions for Bayesian inference, e.g. see [22, 47, 19, 17, 26, 13, 20, 43].”
Advances in Variational Inference (2017, background): “Implicit distributions for VI is an active area of research [72], [81], [102], [105], [107], [118], [129], [196], [210].”
Generative Adversarial Networks (GANs) (2020, background): “The density ratio trick is widely used [4][119][72], [73], [133], [134][135] where class probability estimation is the most popular approach.”
Variational Inference using Implicit Distributions (2017, background): “Finally, Karaletsos (2016) proposed variational message passing, in which adversaries are employed to minimise local Jensen-Shannon divergences in an algo-rithm more akin to expectation propagation (Minka, 2001) than to variational inference.”
Bayesian GAN (2017, methodology): “…recent pre-print Tran et al. (2017) briefly mention using a variational approach to marginalize weights in a GAN, as part of a general exposition on hierarchical implicit models (see also Karaletsos (2016) for a nice theoretical exploration of related topics in graphical model message passing).”
Hierarchical Adversarially Learned Inference (2018, background): “Karaletsos (2016) presents a theoretical framework to jointly train inference networks and generators deﬁned on directed acyclic graphs by leverage multiple discriminators deﬁned nodes and their parents.”
Debiasing Evidence Approximations: On Importance-weighted Autoencoders and Jackknife Variational Inference (2018, methodology): “, 2017), implicit variational models (Huszár, 2017), and adversarial message passing approximations (Karaletsos, 2016).”
Learning Model Reparametrizations: Implicit Variational Inference by Fitting MCMC distributions (2017, methodology): “For instance, recent implicit variational methods [18, 23, 16, 39] that utilise arbitrarily flexible parametric families for q(z;θ) require the computation of log density ratios [37], which is a very difficult problem in high dimensional settings.”