# Sample Efficient Learning of Factored Embeddings of Tensor Fields

arXiv: https://arxiv.org/abs/2209.00372 · HTML: https://mlsanity.com/paper/2209.00372/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 1 Sep 2022.

## Builds on (most cited first, 17 of 17)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Soft Actor-Critic for Discrete Action Settings](https://mlsanity.com/paper/1910.07207/) (2019)
- [Dimensionality Reduction for k-Means Clustering and Low Rank Approximation](https://mlsanity.com/paper/1410.6801/) (2014)
- [Relative Error Tensor Low Rank Approximation](https://mlsanity.com/paper/1704.08246/) (2017)
- [Practical sketching algorithms for low-rank matrix approximation](https://mlsanity.com/paper/1609.00048/) (2016)
- [Optimal Principal Component Analysis in Distributed and Streaming Models](https://mlsanity.com/paper/1504.06729/) (2015)
- [Fast and Guaranteed Tensor Decomposition via Sketching](https://mlsanity.com/paper/1506.04448/) (2015)
- [Low-Rank Tucker Approximation of a Tensor From Streaming Data](https://mlsanity.com/paper/1904.10951/) (2019)
- [Scalable Tucker Factorization for Sparse Tensors - Algorithms and Discoveries](https://mlsanity.com/paper/1710.02261/) (2017)
- [Thompson Sampling via Local Uncertainty](https://mlsanity.com/paper/1910.13673/) (2019)
- [FREDE: Anytime Graph Embeddings](https://mlsanity.com/paper/2006.04746/) (2020)
- [Decomposition of Big Tensors With Low Multilinear Rank](https://mlsanity.com/paper/1412.1885/) (2014)
- [Tensor Random Projection for Low Memory Dimension Reduction](https://mlsanity.com/paper/2105.00105/) (2021)
- [Sparse Hierarchical Tucker Factorization and its Application to Healthcare](https://mlsanity.com/paper/1610.07722/) (2016)

## Abstract (arXiv)

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.