Proposal of Energy-Based Contiuous Time Series Model and Its State Estimation method

Abstract

This paper presents novel energy-based probability model of continuous time series that consists of stochastic process in its hidden dynamics. The formulation of the model enables us to sample the hidden dynamics via common back-propagation and Langevin dynamics, which is derivative method of stochastic gradient descent. General time series model has been studied due to its vast amount of application domain such as human pose estimation, financial prediction, robot’s action planning in the real world. Stochastic process is expected to be a general model for the time series and has been studied well for this sake. However, the existing studies suffers from the problem in the estimation of the state on hidden dynamics due to its complicated nature. This study gives one solution to this issue on which the estimation can be done as a sampling from a joint probability model with well studied sampling method that relays on solely gradient of the energy. Experimental results show the proposed model fit the given synthetic data with the proposed sampling method.