Probabilistic Error Bounds for Low-Rank Tensor Decompositions Used in Large-Scale Data Analysis Applications (LDRD Final Report)

This report documents a research project on analyzing low-rank tensor models for data analysis that took place at Sandia National Laboratories from October 2023–September 2025. The focus of this work was to extend theoretical frameworks from statistics and probability theory for use with models for scalar, vector, and matrix data to models with tensor, or general multi-dimensional array, data. Through this work, we have provided a new set of tools for bounding errors on low-rank tensor models of both complete and sampled data. The remainder of this report is organized as follows. In Section 1, we describe the proposed work at the start of the project. Section 2 describes the research advances made as part of the project. Other research contributions in the form of conference presentations and software development is provided in Section 3. Workforce development at Sandia and Florida Atlantic University (via a subcontract on this project) is provided in Section 4.. Authors: Dunlavy, Daniel Michael [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)] (ORCID:0009000322994798); Lehoucq, Richard B. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)]; Llosa-Vite, Carlos [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)]; Lopez, Oscar F. [Florida Atlantic Univ., Boca Raton, FL (United States)]; Prasadan, Arvind [Sandia National Laboratories (SNL-CA), Livermore, CA (United States)] (ORCID:0000000225217113). DOE Contract: NA0003525. Subjects: 97 MATHEMATICS AND COMPUTING