Time-efficient Bayesian Inference for a (Skewed) von Mises Distribution on the Torus in a Deep Probabilistic Programming Language
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Time-efficient Bayesian Inference for a (Skewed) von Mises Distribution on the Torus in a Deep Probabilistic Programming Language. / Ronning, Ola; Ley, Christophe; Mardia, Kanti V.; Hamelryck, Thomas.
2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI). IEEE, 2021. p. 1-8.Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - Time-efficient Bayesian Inference for a (Skewed) von Mises Distribution on the Torus in a Deep Probabilistic Programming Language
AU - Ronning, Ola
AU - Ley, Christophe
AU - Mardia, Kanti V.
AU - Hamelryck, Thomas
N1 - Publisher Copyright: © 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - 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].
AB - 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].
UR - http://www.scopus.com/inward/record.url?scp=85122864465&partnerID=8YFLogxK
U2 - 10.1109/MFI52462.2021.9591184
DO - 10.1109/MFI52462.2021.9591184
M3 - Article in proceedings
AN - SCOPUS:85122864465
SP - 1
EP - 8
BT - 2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI)
PB - IEEE
T2 - 2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, MFI 2021
Y2 - 23 September 2021 through 25 September 2021
ER -
ID: 291541939