Generalized Energy Based Models

We introduce the Generalized Energy Based Model (GEBM) for generative modelling. These models combine two trained components: a base distribution (generally an implicit model), which can learn the support of data with low intrinsic dimension in a high dimensional space; and an energy function, to refine the probability mass on the learned support. Both the energy function and base jointly constitute the final model, unlike GANs, which retain only the base distribution (the "generator"). GEBMs are trained by alternating between learning the energy and the base. We show that both training stages are well-defined: the energy is learned by maximising a generalized likelihood, and the resulting energy-based loss provides informative gradients for learning the base. Samples from the posterior on the latent space of the trained model can be obtained via MCMC, thus finding regions in this space that produce better quality samples. Empirically, the GEBM samples on image-generation tasks are of much better quality than those from the learned generator alone, indicating that all else being equal, the GEBM will outperform a GAN of the same complexity. When using normalizing flows as base measures, GEBMs succeed on density modelling tasks, returning comparable performance to direct maximum likelihood of the same networks

Flow-GAN: Combining Maximum Likelihood and Adversarial Learning in Generative Models

Adversarial learning of probabilistic models has recently emerged as a promising alternative to maximum likelihood. Implicit models such as generative adversarial networks (GAN) often generate better samples compared to explicit models trained by maximum likelihood. Yet, GANs sidestep the characterization of an explicit density which makes quantitative evaluations challenging. To bridge this gap, we propose Flow-GANs, a generative adversarial network for which we can perform exact likelihood evaluation, thus supporting both adversarial and maximum likelihood training. When trained adversarially, Flow-GANs generate high-quality samples but attain extremely poor log-likelihood scores, inferior even to a mixture model memorizing the training data; the opposite is true when trained by maximum likelihood. Results on MNIST and CIFAR-10 demonstrate that hybrid training can attain high held-out likelihoods while retaining visual fidelity in the generated samples.Comment: AAAI 201

Adversarial Variational Optimization of Non-Differentiable Simulators

Complex computer simulators are increasingly used across fields of science as generative models tying parameters of an underlying theory to experimental observations. Inference in this setup is often difficult, as simulators rarely admit a tractable density or likelihood function. We introduce Adversarial Variational Optimization (AVO), a likelihood-free inference algorithm for fitting a non-differentiable generative model incorporating ideas from generative adversarial networks, variational optimization and empirical Bayes. We adapt the training procedure of generative adversarial networks by replacing the differentiable generative network with a domain-specific simulator. We solve the resulting non-differentiable minimax problem by minimizing variational upper bounds of the two adversarial objectives. Effectively, the procedure results in learning a proposal distribution over simulator parameters, such that the JS divergence between the marginal distribution of the synthetic data and the empirical distribution of observed data is minimized. We evaluate and compare the method with simulators producing both discrete and continuous data.Comment: v4: Final version published at AISTATS 2019; v5: Fixed typo in Eqn 1