Sample Efficient Learning of Factored Embeddings of Tensor Fields

TL;DR

This paper introduces a method for efficiently learning compact, factored embeddings of large tensor fields, enabling faster and more resource-effective data querying and processing in scientific and medical applications.

Contribution

It presents a novel, sample-efficient approach to tensor sketching using Tucker decomposition and stochastic Thompson sampling, improving scalability and accuracy.

Findings

Achieves optimal rank-r Tucker tensor sketches from sub-sampled slices.

Provides a space and time-efficient embedding for large tensor fields.

Enables customizable accuracy in tensor data analysis.

Abstract

Data tensors of orders 2 and greater are now routinely being generated. These data collections are increasingly huge and growing. Many scientific and medical data tensors are tensor fields (e.g., images, videos, geographic data) in which the spatial neighborhood contains important information. 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 tensor fields. All information querying and post-processing on the original tensor field can now be achieved more efficiently and with customizable accuracy as they are performed on these compact factored sketches in latent generative space. We produce optimal rank-r sketchy Tucker decomposition of arbitrary order data tensors by building compact factor matrices 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.