Lecture slides from two guest lectures on tensor-variate data analysis, delivered in STAT 5010: Multivariate Statistical Methods, Spring 2025, Iowa State University (instructed by Prof. Ranjan Maitra).
These slides cover the statistical analysis of tensor-variate (multi-dimensional array) data, from foundational distribution theory to computational methods for high-dimensional applications like fMRI. The lectures were designed for masters and PhD students with a background in multivariate statistics but no prior exposure to tensor methods.
- Tensor basics: notation, modes, unfolding, vectorization
- Tucker decomposition
- Tensor normal distribution and its properties
- Tensor-on-tensor regression
- Matrix-free computational methods for tensor models
- Application to functional MRI data
- Tensor network diagrams
The first lecture covers foundations (tensor algebra, distributions, decompositions) and the second covers regression, computational simplifications, and applications.
- Pal, S., Maitra, R., ToTTR: Tensor-on-Tensor Time Series Regression for Integrated One-step fMRI analysis (in preparation).
- Pal, S., Lahiri, S., Maitra, R., Theoretical Framework for Tensor-on-Tensor Time Series Regression (in preparation).
- Pal, S., Dutta, S., Maitra, R. (2023), Fast matrix-free methods for model-based personalized synthetic MR imaging, Journal of Computational and Graphical Statistics, 33(3): 1109-1117. DOI.
Subrata Pal, Department of Neurology, Washington University in St. Louis.