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 -