Energy-Based Continuous Time Series Probability Model with Latent Stochastic Process

Astract- This paper presents a new energy-based continuous time series probability model that has stochastic process in its latent dynamics. Because the model assuming its output is used for connecting a vector space such as embedding space and latent dynamics, one of the possible application of the present study is to predict sequence of segments such as in the human motion behavior recognition. The present model gives joint distribution of all variable, therefore, it has the property to generate learned sequence without conditioning any values including initial state. This property overcomes existing problem in initial value condition for frequently applied time series model such as recurrent neural network. Furthermore, energy-based continuous formulation gives us consistent method for both learning and estimating the state by the gradient descent and its derivative methods. Such consistent method is not proposed in existing study. In this paper, the model formulation, gradient estimator, and its learning method is shown. Experiments on synthetic data is given, and the validity of the proposed model and method discussed.