VAEs and Flows are two of the most popular methods for density estimation (well, except GANs I guess, but nevermind... 😱). In this work we will argue they are really two sides of the same coin. A flow is based on deterministically transforming an input density through an invertible transformation to a target density. If the transformation changes a volume element we pick up a log-Jacobian term. After decomposing the ELBO in the only way that was not yet considered in the literature, we find that the log-Jacobian corresponds to log[p(x|z)/q(z|x)] of a VAE, where the maps q and p are now stochastic. This suggests a third possibility that bridges the gap between the two: a surjective map which is deterministic and surjective in one direction, and probabilistic in the reverse direction. We find that these ideas unify many methods out there in the literature, such as dequantization, and augmented flows, and we also add a few new methods of our own based on our SurVAE Flows framework. If time permits I will also say a few words on a new type of flow based on the exponential map which is trivially invertible and adds a new tool to the invertible flows toolbox.

Joint work with Didrik Nielsen, Priyank Jaini, Emiel Hoogeboom.

[ video ]

[ video ]

[ video ]

[ video ]

Detecting distribution shift is crucial for ensuring the safety and integrity of autonomous systems and computational pipelines. Recent advances in deep generative models (DGMs) make them attractive for this use case. However, their application is not straightforward: DGMs fail to detect distribution shift when using naive likelihood thresholds. In this talk, I synthesize the recent literature on using DGMs for out-of-distribution detection. I categorize techniques into two broad classes: model-selection and omnibus methods. I close the talk by arguing that many real-world, safety-critical scenarios require the latter approach.

This talk will review recent work on the representational limitations of invertible models both in the context of neural ODEs and normalizing flows. In particular, it has been shown that invertible neural networks are topology preserving and can therefore not map between spaces with different topologies. This has both theoretical and numerical consequences. In the context of normalizing flows for example, the source and target density often have different topologies leading to numerically ill-posed models and training. On top of reviewing the theoretical and practical aspects of this, the talk will also cover several recent models, methods and ideas for alleviating some of these limitations.

[ video ]

[ video ]

[ video ]

[ video ]

[ video ]

[ video ]

Variational inference (VI) plays an essential role in approximate Bayesian inference due to its computational efficiency and broad applicability. Crucial to the performance of VI is the selection of the associated divergence measure, as VI approximates the intractable distribution by minimizing this divergence. In this talk, I will discuss variational inference with different divergence measures first. Then, I will present a new meta-learning algorithm to learn the divergence metric suited for the task of interest, automating the design of VI methods.

Parameterizing latent variable models with deep neural networks has become a major approach to probabilistic modeling. The usual way of fitting these deep latent variable models is to use maximum likelihood. This gives rise to variational autoencoders (VAEs). They jointly learn an approximate posterior distribution over the latent variables and the model parameters by maximizing a lower bound to the log-marginal likelihood of the data. In this talk, I will present an alternative approach to fitting parameters of deep latent-variable models. The idea is to marry adversarial learning and entropy regularization. The family of models fit with this procedure is called Prescribed Generative Adversarial Networks (PresGANs). I will describe PresGANs and discuss how they generate samples with high perceptual quality while avoiding the ubiquitous mode collapse issue of GANs.

[ video ]

Statistical inference is at the heart of the scientific method, and the likelihood function is at the heart of statistical inference. However, many scientific theories are formulated as mechanistic models that do not admit a tractable likelihood. While traditional approaches to confronting this problem may seem somewhat naive, they reveal numerous other considerations in the scientific workflow beyond the approximation error of the likelihood. I will highlight how normalizing flows and other techniques from machine learning are impacting scientific practice, discuss current challenges for state-of-the-art methods, and identify promising new directions in this line of research.

I give an overview of the many uses of flows in probabilistic modeling and inference. I focus on settings in which flows are used to speed up or otherwise improve inference (i.e. settings in which flows are not part of the model specification), including applications to Optimal Experimental Design, Hamiltonian Monte Carlo, and Likelihood-Free Inference. I conclude with a brief discussion of how flows enter into probabilistic programming language (PPL) systems and suggest research directions that are important for improved PPL integration.

[ video ]

to join the slack, please use the link https://join.slack.com/t/innf2020/shared_invite/zt-fp5gvn7l-1XAZrKGL1xtIP03Fsd5ZQQ

Author's availability and zoom link https://docs.google.com/spreadsheets/d/1HJa8F0bMSlM2qQ9WNCJ3LO26hVmndhrFzcgDZPz_VtQ/edit?usp=sharing