STA 790-1 Special Topics: Tensor Methods in Statistics

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Course information

• Instructor: Peter Hoff
• Lecture: MW 10:05-11:20, Old Chem 101
  
• Office hours: Tue 9:30-10:30 AM Rm 219

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Course outline

1. Methods for a single matrix
   1. SVD
   2. GSVD
   3. AMMI
2. Method for multiple matrices
   1. shared subspaces
   2. GLRAM
   3. multilinear models
3. Tensor methods
   1. tensor decompositions
   2. multilinear models
   3. methods via invariance

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Reading

• Hoff MVA lecture notes: pca, svd, multilinear models
• Gabriel [1978]: Least Squares Approximation of Matrices by Additive and Multiplicative Models
• Tsukuma [2008]: Admissibility and minimaxity of Bayes estimators for a normal mean matrix
• Allen, Grosenick and Taylor [2014]: A GLS matrix decomposition
• Bach [2008]: Consistency of trace norm minimization
• Josee and Sardy [2016]: Adaptive shrinkage of singular values
• Gavish and Donoho [2017]: Optimal shrinkage of singular values
• Sheehan and Saad [2007]: HOOI and its relation to PCA and GLRAM
• Lim [2013]: Tensors and hypermatrices
• Kolda and Bader [2009]: Tensor decompositions and applications

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Other materials

• Exercises
• Notes: svd, matrix models, sv shrinkage, multilinear matrix models, tensor operations, tensor covariance, multilinear regression and tsvd, tensor svd
• Image compression example: slides, code, data
• Audio spectrogram example: code
• Air quality example: slides, code, data