Low Rank Tensor Methods in High Dimensional Data Analysis

Delve into the second part of a comprehensive lecture on low rank tensor methods in high-dimensional data analysis. Explore advanced concepts such as ODECO decomposition, computational limits, spectral initialization, and tensor regression. Gain insights into the challenges and recent progress in analyzing multidimensional data from diverse fields like chemometrics, genomics, physics, and signal processing. Learn about novel statistical methods, efficient computational algorithms, and fundamental mathematical theory for extracting useful information from large-scale tensor data. Discover applications in spatio-temporal transcriptome analysis of the brain and low rank matrix estimation. Suitable for researchers and practitioners working with high-dimensional data and tensor methods.

OVERVIEW
ODECO DECOMPOSITION
GENERAL STRATEGY
COMPUTATIONAL LIMITS
WHY IS IT DIFFICULT?
SPECTRAL INITIALIZATION
SNR FOR ODECO
SPATIO-TEMPORAL TRANSCRIPTOME OF THE BRAIN
SUMMARY
TENSOR REGRESSION
TUCKER RANK
CONVEX REGULARIZATION
EXAMPLES SPARSITY
Low RANK MATRIX ESTIMATION
DECOMPOSABILITY