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

Learning Generative Embeddings using an Optimal Subsampling Policy for Tensor Sketching