Leveraging Latent Space Symmetry for Time Series Prediction

Abstract

In machine learning, exploiting symmetry in data is crucial to improving both learning efficiency and accuracy. Symmetry detection algorithms in time series data have received much attention in unsupervised learning to uncover the core physical principles of the data. Most existing work focuses on basic two-dimensional symmetry and is inadequate to handle more complex forms, such as the three-dimensional rotations that are common in real-world scenarios. To overcome this limitation, we introduce a new model that can learn such complex symmetries in uniformly varying time series data. Unlike conventional approaches that exploit symmetries in data space, our model adopts a latent variable framework and assumes existing symmetries in this latent space. By applying the identifiability theory of nonlinear ICA, we theoretically and experimentally prove that the symmetries detected by our method are consistent with the true symmetries from time series data whose symmetries are broken in data space.