CTT: Causally Informed Tensor Train Decomposition

Tensor Train (TT) is a tensor decomposition technique designed to resolve the curse of dimensionality and the intermediate memory blow-up problems in traditional techniques for high-dimensional data analysis. Tensor train process provides linear space complexity by creating a sequential tensor network of low modalities. However, the selected sequence of decomposition order can have a significant impact on the accuracy and representativeness of the final decomposition and, unfortunately, choosing a good order for the TT representation is not a trivial task. In this paper, we observe that the causal structure underlying the data can impact the tensor train process and that a rough estimate of causality can be used to inform the order of the latent spaces to consider. Enlightened by this observation, we propose a novel causally informed tensor train decomposition (CTT) approach to tackle the sequence selection problem in TT-decomposition. CTT leverages the structural information in a given causal graph and recommends a suitable causally-informed decomposition sequence for TT-decomposition.