Seminar by Dr. Kwangmin Lee
- 【Date&Time】
- 26 August,2025 (Tuesday) 11:00-12:00
Admission Free, No Booking Necessary
- 【Place】
- Seminar Room 5 (D313,314), The Institute of Statistical Mathematics
- 【Speaker】
- Kwangmin Lee（Chonnam National University）
- 【Title】
- Spiked Covariance Inference with Bias Correction under an Inverse-Wishart Prior
- 【Abstract】
- We study Bayesian inference in the spiked covariance model, where a small number of spiked eigenvalues dominate the spectrum. Our goal is to infer the spiked eigenvalues, their corresponding eigenvectors, and the number of spikes, providing a Bayesian solution to principal component analysis with uncertainty quantification.
We place an inverse-Wishart prior on the covariance matrix to derive posterior distributions for the spiked eigenvalues and eigenvectors. Although posterior sampling is computationally efficient due to conjugacy, we identify a bias in the posterior eigenvalue estimates in high-dimensional settings. To address this, we propose two complementary bias correction strategies: (i) a hyperparameter adjustment method, and (ii) a post-hoc multiplicative correction. For inferring the number of spikes, we develop a BIC-type approximation to the marginal likelihood and prove posterior consistency in the high-dimensional regime p>n. Furthermore, we establish concentration inequalities and posterior contraction rates for the leading eigenstructure, demonstrating minimax optimality for the spiked eigenvector in the single-spike case. Simulation studies and real data applications show that our method outperforms existing approaches, particularly in accurately quantifying uncertainty in both eigenstructure estimation and spike number selection.
