Extending Stan for Deep Probabilistic Programming

Stan is a popular declarative probabilistic programming language with a high-level syntax for expressing graphical models and beyond. Stan differs by nature from generative probabilistic programming languages like Church, Anglican, or Pyro. This paper presents a comprehensive compilation scheme to compile any Stan model to a generative language and proves its correctness. This sheds a clearer light on the relative expressiveness of different kinds of probabilistic languages and opens the door to combining their mutual strengths. Specifically, we use our compilation scheme to build a compiler from Stan to Pyro and extend Stan with support for explicit variational inference guides and deep probabilistic models. That way, users familiar with Stan get access to new features without having to learn a fundamentally new language. Overall, our paper clarifies the relationship between declarative and generative probabilistic programming languages and is a step towards making deep probabilistic programming easier

VAE with a VampPrior

Many different methods to train deep generative models have been introduced in the past. In this paper, we propose to extend the variational auto-encoder (VAE) framework with a new type of prior which we call "Variational Mixture of Posteriors" prior, or VampPrior for short. The VampPrior consists of a mixture distribution (e.g., a mixture of Gaussians) with components given by variational posteriors conditioned on learnable pseudo-inputs. We further extend this prior to a two layer hierarchical model and show that this architecture with a coupled prior and posterior, learns significantly better models. The model also avoids the usual local optima issues related to useless latent dimensions that plague VAEs. We provide empirical studies on six datasets, namely, static and binary MNIST, OMNIGLOT, Caltech 101 Silhouettes, Frey Faces and Histopathology patches, and show that applying the hierarchical VampPrior delivers state-of-the-art results on all datasets in the unsupervised permutation invariant setting and the best results or comparable to SOTA methods for the approach with convolutional networks.Comment: 16 pages, final version, AISTATS 201

Resampled Priors for Variational Autoencoders

We propose Learned Accept/Reject Sampling (LARS), a method for constructing richer priors using rejection sampling with a learned acceptance function. This work is motivated by recent analyses of the VAE objective, which pointed out that commonly used simple priors can lead to underfitting. As the distribution induced by LARS involves an intractable normalizing constant, we show how to estimate it and its gradients efficiently. We demonstrate that LARS priors improve VAE performance on several standard datasets both when they are learned jointly with the rest of the model and when they are fitted to a pretrained model. Finally, we show that LARS can be combined with existing methods for defining flexible priors for an additional boost in performance

Normalizing Flow with Variational Latent Representation

Normalizing flow (NF) has gained popularity over traditional maximum likelihood based methods due to its strong capability to model complex data distributions. However, the standard approach, which maps the observed data to a normal distribution, has difficulty in handling data distributions with multiple relatively isolated modes. To overcome this issue, we propose a new framework based on variational latent representation to improve the practical performance of NF. The idea is to replace the standard normal latent variable with a more general latent representation, jointly learned via Variational Bayes. For example, by taking the latent representation as a discrete sequence, our framework can learn a Transformer model that generates the latent sequence and an NF model that generates continuous data distribution conditioned on the sequence. The resulting method is significantly more powerful than the standard normalization flow approach for generating data distributions with multiple modes. Extensive experiments have shown the advantages of NF with variational latent representation.Comment: 24 pages, 7 figure