Tensor decomposition for multi-context data analysis

Across scientific domains, a fundamental challenge is to understand how systems change across contexts. Examples include biological processes across diseases or word meanings across genres of text. Tensors are a natural framework to study such multi-context systems, generalizing the role of matrices and linear algebra in classical data analysis methods such as principal component analysis. The investigator will design new tensor decomposition algorithms and use them to analyze multi-context data. Special attention will be paid to the theoretical guarantees of the algorithms, to ensure their reliability. The algorithms will be used to improve artificial intelligence models to study variability of gene programs across diseases and of word usage across literary genres. The project will implement new tensor decomposition algorithms and prove results that justify their design and explain their performance. A longstanding challenge in the theory and practice of tensor decomposition is that the higher-order power method cannot find a low rank decomposition: for tensors (unlike matrices) computing a best rank one approximation and deflating (subtracting it off) usually fails: the deflation step leaves the rank unchanged or even increases the rank. The proposed algorithms will address this problem by transforming a tensor to a special basis before computing its decomposition. Numerical analysis and real algebraic geometry will be used to establish the theoretical guarantees of the procedures. The methods will build a tensor decomposition one term at a time. This is more scalable, reliable, and interpretable than computing all terms at once, and yields decompositions that are compatible across ranks. Tensor decomposition enables the simultaneous comparison of data across contexts, without requiring pairwise comparison of contexts or that samples are measured in multiple contexts. The investigator will apply the algorithms to analyze multi-context gene expression data and contextualized word embeddings. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2608217 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Anna Seigal | Institution: Harvard University, CAMBRIDGE, MA | Award Amount: $400,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2608217 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2608217.html