Summary of Structured Matrix Learning Under Arbitrary Entrywise Dependence and Estimation Of Markov Transition Kernel, by Jinhang Chai et al.
Structured Matrix Learning under Arbitrary Entrywise Dependence and Estimation of Markov Transition Kernel
by Jinhang Chai, Jianqing Fan
First submitted to arxiv on: 4 Jan 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST)
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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 proposed framework for noisy low-rank-plus-sparse matrix recovery tackles the challenge of structured matrix estimation under general noise dependence assumptions, departing from previous work that assumed strong noise dependence. The incoherent-constrained least-square estimator is introduced and its tightness is established via a novel result demonstrating the energy spreading phenomenon across entries of two arbitrary low-rank incoherent matrices. This framework has far-reaching implications for statistical machine learning, with applications to estimating structured Markov transition kernels, conditional mean operators, multitask regression, and structured covariance estimation. To tackle the potentially hard optimization problem, an alternating minimization algorithm is proposed. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper solves a big math problem that helps machines learn from noisy data. It’s like trying to see through fog – you need to understand how noise affects the signal. The researchers came up with a new way to deal with this noise and showed it can be used for lots of important problems, like learning how things move or understanding patterns in data. |
Keywords
* Artificial intelligence * Machine learning * Optimization * Regression
