Learning Generative Embeddings using an Optimal Subsampling Policy for Tensor Sketching

Data tensors of orders 3 and greater are routinely being generated. These data collections are increasingly huge and growing. They are either tensor fields (e.g., images, videos, geographic data) in which each location of data contains important information or permutation invariant general tensors (e.g., unsupervised latent space learning, graph network analysis, recommendation systems, etc.). Directly accessing such large data tensor collections for information has become increasingly prohibitive. We learn approximate full-rank and compact tensor sketches with decompositive representations providing compact space, time and spectral embeddings of both tensor fields (P-SCT) and general tensors (P-SCT-Permute). All subsequent information querying with high accuracy is performed on the generative sketches. We produce optimal rank-r Tucker decompositions of arbitrary order data tensors by building tensor sketches from a sample-efficient sub-sampling of tensor slices. Our sample efficient policy is learned via an adaptable stochastic Thompson sampling using Dirichlet distributions with conjugate priors.