Blind Minimax Estimation

We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose parameter set is itself estimated from measurements. Thus, one does not require any prior assumption or knowledge, and the proposed estimator can be applied to any linear regression problem. We demonstrate analytically that the BMEs strictly dominate the least-squares estimator, i.e., they achieve lower mean-squared error for any value of the parameter vector. Both Stein's estimator and its positive-part correction can be derived within the blind minimax framework. Furthermore, our approach can be readily extended to a wider class of estimation problems than Stein's estimator, which is defined only for white noise and non-transformed measurements. We show through simulations that the BMEs generally outperform previous extensions of Stein's technique.Comment: 12 pages, 7 figure

Semi-Supervised Single- and Multi-Domain Regression with Multi-Domain Training

We address the problems of multi-domain and single-domain regression based on distinct and unpaired labeled training sets for each of the domains and a large unlabeled training set from all domains. We formulate these problems as a Bayesian estimation with partial knowledge of statistical relations. We propose a worst-case design strategy and study the resulting estimators. Our analysis explicitly accounts for the cardinality of the labeled sets and includes the special cases in which one of the labeled sets is very large or, in the other extreme, completely missing. We demonstrate our estimators in the context of removing expressions from facial images and in the context of audio-visual word recognition, and provide comparisons to several recently proposed multi-modal learning algorithms.Comment: 24 pages, 6 figures, 2 table

Robust estimation in flat fading channels under bounded channel uncertainties

Cataloged from PDF version of article.We investigate channel equalization problem for time-varying flat fading channels under bounded channel uncertainties. We analyze three robust methods to estimate an unknown signal transmitted through a time-varying flat fading channel. These methods are based on minimizing certain meansquare error criteria that incorporate the channel uncertainties into their problem formulations instead of directly using the inaccurate channel information that is available. We present closed-form solutions to the channel equalization problems for each method and for both zero mean and nonzero mean signals. We illustrate the performances of the equalization methods through simulations. © 2013 Elsevier Inc. All rights reserved