Covariance thresholding, kernel random matrices and sparse PCA
In Sparse Principal Component Analysis (PCA) we wish to reconstruct a low-rank matrix from noisy observations, under sparsity assumptions on the factors recovered. Johnstone and Lu (2004) formalized these assumptions in the ‘spiked covariance model’, wherein we observe $n$ i.i.d. samples from a $p$ dimensional Gaussian distribution $N(0, I + …