期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2014
卷号：111
期号：4
页码：1253-1258
DOI：10.1073/pnas.1219097111
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：In a broad range of classification and decision-making problems, one is given the advice or predictions of several classifiers, of unknown reliability, over multiple questions or queries. This scenario is different from the standard supervised setting, where each classifier's accuracy can be assessed using available labeled data, and raises two questions: Given only the predictions of several classifiers over a large set of unlabeled test data, is it possible to (i) reliably rank them and (ii) construct a metaclassifier more accurate than most classifiers in the ensemble? Here we present a spectral approach to address these questions. First, assuming conditional independence between classifiers, we show that the off-diagonal entries of their covariance matrix correspond to a rank-one matrix. Moreover, the classifiers can be ranked using the leading eigenvector of this covariance matrix, because its entries are proportional to their balanced accuracies. Second, via a linear approximation to the maximum likelihood estimator, we derive the Spectral Meta-Learner (SML), an unsupervised ensemble classifier whose weights are equal to these eigenvector entries. On both simulated and real data, SML typically achieves a higher accuracy than most classifiers in the ensemble and can provide a better starting point than majority voting for estimating the maximum likelihood solution. Furthermore, SML is robust to the presence of small malicious groups of classifiers designed to veer the ensemble prediction away from the (unknown) ground truth.
