Tensor Graphical Models For Complex And High Dimensional Data
Talkat Algorithmic Advances for Statistical Inference with Combinatorial Structure · 2021-10-11..10-15·
summary
Claims that one can jointly estimate high‑dimensional means and row/column covariances in matrix‑normal/tensor data with provable rates, often matching ID‑sample rates, using a workflow that combines Gemini estimator, graphical Lasso and GLS plus concentration from Hansen–White; theory even allows single‑replicate (n=1) recovery under sparsity for Kronecker‑product models. Implements coordinate‑descent solvers and a Bigraph Lasso for Kronecker‑sum cases; applied to ulcerative colitis arrays it finds three persistent genes and uncovers a steroid‑treatment sample correlation.
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chapters (17)
- 0:00Start
- 3:33Probability Distribution of the Errors
- 11:35Mutual Varied Modeling
- 12:30Conceptual Challenges
- 13:21Chronicle Product of Graphs
- 14:08Classical Gaussian Graphic Model
- 15:32Quantity Product of Graphs
- 32:31Three-Step Procedure
- 34:09Chronicles Sum
- 42:10Simulation Plots
- 42:47Algorithm
- 43:14Centering
- 44:08Inference
- 44:45Global Centering
- 48:36Randomization Theory
- 49:01Summary
- 50:21Conclusion
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