Summary of High-dimensional Tensor Discriminant Analysis with Incomplete Tensors, by Elynn Chen et al.
High-Dimensional Tensor Discriminant Analysis with Incomplete Tensors
by Elynn Chen, Yuefeng Han, Jiayu Li
First submitted to arxiv on: 18 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Methodology (stat.ME)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper introduces a novel approach to tensor classification with incomplete data, framed within high-dimensional tensor linear discriminant analysis. It proposes the Tensor Linear Discrimant Analysis with Missing Data (Tensor LDA-MD) algorithm, which manages high-dimensional tensor predictors with missing entries by leveraging the decomposable low-rank structure of the discriminant tensor. The authors establish convergence rates for the estimation error of the discriminant tensor and minimax optimal bounds for the misclassification rate, addressing key gaps in the literature. Additionally, they derive large deviation bounds for the generalized mode-wise sample covariance matrix and its inverse, which are crucial tools in their analysis. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper solves a big problem: how to classify things when some of the information is missing. Right now, we don’t have good ways to do this, especially when dealing with really big amounts of data. The authors created a new method called Tensor LDA-MD that can handle missing data and does it well. They also showed that their method works by testing it on simulations and real data. |
Keywords
» Artificial intelligence » Classification
