Minimax Lower Bounds for Noisy Matrix Completion Under Sparse Factor Models

Minimax Lower Bounds for Noisy Matrix Completion Under Sparse Factor Models

This paper examines fundamental error characteristics for a general class of matrix completion problems, where matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our main contributions come in the form of minimax lower bounds for the expected per-element squared error for these problems under several noise/corruption models;...

Minimax Bounds for Sparse Pca with Noisy High-dimensional Data.

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the l2 loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the ris...

Minimax lower bounds for estimation

Minimax lower bounds

Now that we have a good handle on the performance of ERM and its variants, it is time to ask whether we can do better. For example, consider binary classification: we observe n i.i.d. training samples from an unknown joint distribution P on X× {0,1}, where X is some feature space, and for a fixed class F of candidate classifiers f :X→ {0,1} we let f̂n be the ERM solution f̂n = argmin f ∈F 1 n n ∑...

Minimax Lower Bounds

Minimax Lower Bounds Adityanand Guntuboyina 2011 This thesis deals with lower bounds for the minimax risk in general decision-theoretic problems. Such bounds are useful for assessing the quality of decision rules. After providing a unified treatment of existing techniques, we prove new lower bounds which involve f -divergences, a general class of dissimilarity measures between probability measu...