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Understanding the dynamics of a system is important in many scientific andengineering domains. This problem can be approached by learning statetransition rules from observations using machine learning techniques. Suchobserved time-series data often consist of sequences of many continuousvariables with noise and ambiguity, but we often need rules of dynamics thatcan be modeled with a few essential variables. In this work, we propose amethod for extracting a small number of essential hidden variables fromhigh-dimensional time-series data and for learning state transition rulesbetween these hidden variables. The proposed method is based on the RestrictedBoltzmann Machine (RBM), which treats observable data in the visible layer andlatent features in the hidden layer. However, real-world data, such as videoand audio, include both discrete and continuous variables, and these variableshave temporal relationships. Therefore, we propose Recurrent TemporalGaussianBernoulli Restricted Boltzmann Machine (RTGB-RBM), which combinesGaussian-Bernoulli Restricted Boltzmann Machine (GB-RBM) to handle continuousvisible variables, and Recurrent Temporal Restricted Boltzmann Machine (RT-RBM)to capture time dependence between discrete hidden variables. We also propose arule-based method that extracts essential information as hidden variables andrepresents state transition rules in interpretable form. We conduct experimentson Bouncing Ball and Moving MNIST datasets to evaluate our proposed method.Experimental results show that our method can learn the dynamics of thosephysical systems as state transition rules between hidden variables and canpredict unobserved future states from observed state transitions.

Learning State Transition Rules from Hidden Layers of Restricted Boltzmann Machines