Learning State Transition Rules from High-Dimensional Time Series Data with Recurrent Temporal Gaussian-Bernoulli Restricted Boltzmann Machines

Abstract

Abstract Understanding the dynamics of a system is crucial in various scientific and engineering domains. Machine learning techniques have been employed to learn state transition rules from observed time-series data. However, these data often contain sequences of noisy and ambiguous continuous variables, while we typically seek simplified dynamics rules that capture essential variables. In this work, we propose a method to extract a small number of essential hidden variables from high-dimensional time-series data and learn state transition rules between hidden variables. Our approach is based on the Restricted Boltzmann Machine (RBM), which models observable data in the visible layer and latent features in the hidden layer. However, real-world data, such as video and audio, consist of both discrete and continuous variables with temporal relationships. To address this, we introduce the Recurrent Temporal Gaussian-Bernoulli Restricted Boltzmann Machine (RTGB-RBM), which combines the Gaussian-Bernoulli Restricted Boltzmann Machine (GB-RBM) to handle continuous visible variables and the Recurrent Temporal Restricted Boltzmann Machine (RT-RBM) to capture time dependencies among discrete hidden variables. Additionally, we propose a rule-based method to extract essential information as hidden variables and represent state transition rules in an interpretable form. We evaluate our proposed method on the Bouncing Ball, Moving MNIST, and dSprite datasets. Experimental results demonstrate that our approach effectively learns the dynamics of these physical systems by extracting state transition rules between hidden variables. Moreover, our method can predict unobserved future states based on observed state transitions.

Keywords

• Restricted Boltzmann Machine State Transition Rules Hidden Variables