Inference for Heteroskedastic PCA with Missing Data
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2021
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913736397160448 |
|---|---|
| author | Yan, Yuling Chen, Yuxin Fan, Jianqing |
| author_facet | Yan, Yuling Chen, Yuxin Fan, Jianqing |
| contents | This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly under-explored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in general difficult in high dimension, the challenge is further compounded by the prevalent presence of missing data and heteroskedastic noise. We propose a novel approach to performing valid inference on the principal subspace under a spiked covariance model with missing data, on the basis of an estimator called HeteroPCA (Zhang et al., 2022). We develop non-asymptotic distributional guarantees for HeteroPCA, and demonstrate how these can be invoked to compute both confidence regions for the principal subspace and entrywise confidence intervals for the spiked covariance matrix. Our inference procedures are fully data-driven and adaptive to heteroskedastic random noise, without requiring prior knowledge about the noise levels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_12365 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Inference for Heteroskedastic PCA with Missing Data Yan, Yuling Chen, Yuxin Fan, Jianqing Statistics Theory Information Theory Machine Learning Methodology This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly under-explored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in general difficult in high dimension, the challenge is further compounded by the prevalent presence of missing data and heteroskedastic noise. We propose a novel approach to performing valid inference on the principal subspace under a spiked covariance model with missing data, on the basis of an estimator called HeteroPCA (Zhang et al., 2022). We develop non-asymptotic distributional guarantees for HeteroPCA, and demonstrate how these can be invoked to compute both confidence regions for the principal subspace and entrywise confidence intervals for the spiked covariance matrix. Our inference procedures are fully data-driven and adaptive to heteroskedastic random noise, without requiring prior knowledge about the noise levels. |
| title | Inference for Heteroskedastic PCA with Missing Data |
| topic | Statistics Theory Information Theory Machine Learning Methodology |
| url | https://arxiv.org/abs/2107.12365 |