Bayesian Inference on Hidden Knowledge in High-Throughput Molecular Biology Data
PRICAI '08 Proceedings of the 10th Pacific Rim International Conference on Artificial Intelligence: Trends in Artificial Intelligence
Principal neighborhood dictionaries for nonlocal means image denoising
IEEE Transactions on Image Processing
Mining latent sources of causal time series using nonlinear state space modeling
ACIIDS'11 Proceedings of the Third international conference on Intelligent information and database systems - Volume Part I
Intrinsic dimension estimation by maximum likelihood in isotropic probabilistic PCA
Pattern Recognition Letters
| Hi-index | 35.68 |
The eigenvalue spectrum of covariance matrices is of central importance to a number of data analysis techniques. Usually, the sample covariance matrix is constructed from a limited number of noisy samples. We describe a method of inferring the true eigenvalue spectrum from the sample spectrum. Results of Silverstein (1986), which characterize the eigenvalue spectrum of the noise covariance matrix, and inequalities between the eigenvalues of Hermitian matrices are used to infer probability densities for the eigenvalues of the noise-free covariance matrix, using Bayesian inference. Posterior densities for each eigenvalue are obtained, which yield error estimates. The evidence framework gives estimates of the noise variance and permits model order selection by estimating the rank of the covariance matrix. The method is illustrated with numerical examples