Singular vector and singular subspace distribution for the matrix denoising model

By Z. Bao, Xiucai Ding, Ke Wang. 2018

60 citations recorded by the source corpus.

In this paper, we study the matrix denosing model $Y=S+X$, where $S$ is a low-rank deterministic signal matrix and $X$ is a random noise matrix, and both are $M\times n$. In the scenario that $M$ and $n$ are comparably large and the signals are supercritical, we study the fluctuation of the outlier singular vectors of $Y$. More specifically, we derive the limiting distribution of angles between the principal singular vectors of $Y$ and their deterministic counterparts, the singular vectors of $S$. Further, we also derive the distribution of the distance between the subspace spanned by the principal singular vectors of $Y$ and that spanned by the singular vectors of $S$. It turns out that the limiting distributions depend on the structure of the singular vectors of $S$ and the distribution of $X$, and thus they are non-universal.

Subfields: Mathematical Physics, Radiology, Nuclear Medicine and Imaging, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3cc112e1e0a6e223617c6cf7822d8e5668902810

How researchers see this paper

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In Mathematical Physics

1. Z. Bao
2. Xiucai Ding
3. Ke Wang
4. Jingming Wang
5. Guangming Pan
6. Jun Yin
7. Wang Zhou
8. Natesh S. Pillai

In Statistics and Probability

1. Z. Bao
2. Xiucai Ding
3. Ke Wang
4. Jingming Wang
5. Jun Yin
6. Guangming Pan
7. Wang Zhou
8. Natesh S. Pillai

Citations in the corpus

• Statistical inference for principal components of spiked covariance matrices (2020, methodology): “Similarly to [9], we start with Green function representations of the eigenvector and eigenvalue statistics.”