PSVO: Particle Smoothing Variational Objectives

This code provides a reference implementation of the Smoothing Variational Objectives (SVO) algorithms described in the publications:

• Variational Objectives for Markovian Dynamics with Backwards Simulation. \ Moretti, A.*, Wang, Z.*, Wu, L.*, Drori, I., Pe'er, I. \ European Conference on Artificial Intelligence, 2020.

• Particle Smoothing Variational Objectives. \ Moretti, A.*, Wang, Z.*, Wu, L.*, Drori, I., Pe'er, I. \ arXiv preprint, arXiv:1909.097342019.

• Smoothing Nonlinear Variational Objectives with Sequential Monte Carlo. \ Moretti, A.*, Wang, Z.*, Wu, L., Pe'er, I. \ ICLR Workshop on Deep Generative Models for Highly Structured Data, 2019.

SVO is written as an abstract class that reduces to two related variational inference methods for time series. As a reference, the AESMC and IWAE algorithms are implemented from the following publications:

• Auto-Encoding Sequential Monte Carlo. \ Le, T., Igl, M., Rainforth, T., Jin, T., Wood, F. \ International Conference on Learning Representations, 2018.

• Importance Weighted Autoencoders. \ Burda, Y., Grosse, R., Salakhutidinov, R. \ International Conference on Learning Representations, 2016.

Installation

The code is written in Python 3.6. The following dependencies are required:

• Tensorflow
• seaborn
• numpy
• scipy
• matplotlib

To check out, run git@github.com:amoretti86/psvo.git

Usage

Running python runner_flags.py will find a two dimensional representation of the Fitzhugh-Nagumo dynamical system from one dimensional observations. The following figure provides the original dynamical system and trajectories along with the resulting inferred dynamics and trajectories from SVO.

Demo

Original	Inferred