Time-efficient Bayesian Inference for a (Skewed) von Mises Distribution on the Torus in a Deep Probabilistic Programming Language
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
Probabilistic programming languages (PPLs) are at the interface between statistics and the theory of programming languages. PPLs formulate statistical models as stochastic programs that enable automatic inference algorithms and optimization. Pyro [1] and its sibling NumPyro [2] are PPLs built on top of the deep learning frameworks PyTorch [3] and Jax [4], respectively. Both PPLs provide simple, highly similar interfaces for inference using efficient implementations of Hamiltonian Monte Carlo (HMC), the No-U-Turn Sampler (NUTS), and Stochastic Variational Inference (SVI). They automatically generate variational distributions from a model, automatically enumerate discrete variables, and support formulating deep probabilistic models such as variational autoencoders and deep Markov models. The Sine von Mises distribution and its skewed variant are toroidal distributions relevant to protein bioinformatics. They provide a natural way to model the dihedral angles of protein structures, which is important in protein structure prediction, simulation and analysis. We present efficient implementations of the Sine von Mises distribution and its skewing in Pyro and NumPyro, and devise a simulation method that increases efficiency with several orders of magnitude when using parallel hardware (i.e., modern CPUs, GPUs, and TPUs). We demonstrate the use of the skewed Sine von Mises distribution by modeling dihedral angles of proteins using a Bayesian mixture model inferred using NUTS, exploiting NumPyro's facilities for automatic enumeration [5].
Originalsprog | Engelsk |
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Titel | 2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI) |
Forlag | IEEE |
Publikationsdato | 2021 |
Sider | 1-8 |
ISBN (Elektronisk) | 978-1-6654-4521-4 |
DOI | |
Status | Udgivet - 2021 |
Begivenhed | 2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, MFI 2021 - Karlsruhe, Tyskland Varighed: 23 sep. 2021 → 25 sep. 2021 |
Konference
Konference | 2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, MFI 2021 |
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Land | Tyskland |
By | Karlsruhe |
Periode | 23/09/2021 → 25/09/2021 |
Bibliografisk note
Funding Information:
We would like to thank the Pyro PPL developers Fritz Obermeyer and Du Phat for valuable feedback and discussion about our implementations. We acknowledge support from the Independent Research Fund Denmark (DFF) under the grant ”Deep Probabilistic Programming for Protein Structure Prediction”. K. V. Mardia acknowledges the Leverhulme Trust for the Emeritus Fellowship. Christophe Ley’s research is supported by the FWO Krediet aan Navorsers grant with reference number 1510391N.
Publisher Copyright:
© 2021 IEEE.
ID: 291541939