A NOVEL VARIATIONAL FAMILY FOR HIDDEN NON-LINEAR MARKOV MODELS
Authors: Daniel Hernandez Diaz, Antonio Khalil Moretti, Ziqiang Wei, Shreya Saxena, John Cunningham, Liam Paninski
Keywords: variational inference, time series, nonlinear dynamics, neuroscience
TL;DR: We propose a new variational inference algorithm for time series and a novel variational family  endowed with nonlinear dynamics.
Abstract: Latent variable models have been widely applied for the analysis and visualization of large datasets. In the case of sequential data, closed-form inference is possible when the transition and observation functions are linear. However, approximate inference techniques are usually necessary when dealing with nonlinear evolution and observations. Here, we propose a novel variational inference framework for the explicit modeling of time series, Variational Inference for Nonlinear Dynamics (VIND), that is able to uncover nonlinear observation and latent dynamics from sequential data. The framework includes a structured approximate posterior, and an algorithm that relies on the fixed-point iteration method to find the best estimate for latent trajectories. We apply the method to several datasets and show that it is able to accurately infer the underlying dynamics of these systems, in some cases substantially outperforming state-of-the-art methods.