Inference for Heteroskedastic PCA with Missing Data

Understand

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.