Multi-resolution Tensor Learning for Large-Scale Spatial Data

Abstract

High-dimensional tensor models are notoriously computationally expensive to train. We present a meta-learning algorithm, MMT, that can significantly speed up the process for spatial tensor models. MMT leverages the property that spatial data can be viewed at multiple resolutions, which are related by coarsening and finegraining from one resolution to another. Using this property, MMT learns a tensor model by starting from a coarse resolution and iteratively increasing the model complexity. In order to not "over-train" on coarse resolution models, we investigate an information-theoretic fine-graining criterion to decide when to transition into higher-resolution models. We provide both theoretical and empirical evidence for the advantages of this approach. When applied to two real-world large-scale spatial datasets for basketball player and animal behavior modeling, our approach demonstrate 3 key benefits: 1) it efficiently captures higher-order interactions (i.e., tensor latent factors), 2) it is orders of magnitude faster than fixed resolution learning and scales to very fine-grained spatial resolutions, and 3) it reliably yields accurate and interpretable models.