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Fritz Obermeyer

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3 papers

2 author rows

JMLR Journal 2019 Journal Article

Pyro: Deep Universal Probabilistic Programming

Eli Bingham
Jonathan P. Chen
Martin Jankowiak
Fritz Obermeyer
Neeraj Pradhan
Theofanis Karaletsos
Rohit Singh
Paul Szerlip

Pyro is a probabilistic programming language built on Python as a platform for developing advanced probabilistic models in AI research. To scale to large data sets and high-dimensional models, Pyro uses stochastic variational inference algorithms and probability distributions built on top of PyTorch, a modern GPU-accelerated deep learning framework. To accommodate complex or model-specific algorithmic behavior, Pyro leverages Poutine, a library of composable building blocks for modifying the behavior of probabilistic programs. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2019. ( edit, beta )

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ICML Conference 2019 Conference Paper

Tensor Variable Elimination for Plated Factor Graphs

Fritz Obermeyer
Eli Bingham
Martin Jankowiak
Neeraj Pradhan
Justin T. Chiu
Alexander M. Rush
Noah D. Goodman

A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to plate diagrams for directed graphical models. To exploit efficient tensor algebra in graphs with plates of variables, we generalize undirected factor graphs to plated factor graphs and variable elimination to a tensor variable elimination algorithm that operates directly on plated factor graphs. Moreover, we generalize complexity bounds based on treewidth and characterize the class of plated factor graphs for which inference is tractable. As an application, we integrate tensor variable elimination into the Pyro probabilistic programming language to enable exact inference in discrete latent variable models with repeated structure. We validate our methods with experiments on both directed and undirected graphical models, including applications to polyphonic music modeling, animal movement modeling, and latent sentiment analysis.

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ICML Conference 2018 Conference Paper

Pathwise Derivatives Beyond the Reparameterization Trick

Martin Jankowiak
Fritz Obermeyer

We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise gradients for probability distributions not directly amenable to the reparameterization trick: Gamma, Beta, and Dirichlet. We further observe that when the reparameterization trick is applied to the Cholesky-factorized multivariate Normal distribution, the resulting gradients are suboptimal in the sense of optimal transport. We derive the optimal gradients and show that they have reduced variance in a Gaussian Process regression task. We demonstrate with a variety of synthetic experiments and stochastic variational inference tasks that our pathwise gradients are competitive with other methods.

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