Abstract:
:Maximum likelihood estimators and other direct optimization-based estimators dominated statistical estimation and prediction for decades. Yet, the principled foundations supporting their dominance do not apply to the discrete high-dimensional inference problems of the 21st century. As it is well known, statistical decision theory shows that maximum likelihood and related estimators use data only to identify the single most probable solution. Accordingly, unless this one solution so dominates the immense ensemble of all solutions that its probability is near one, there is no principled reason to expect such an estimator to be representative of the posterior-weighted ensemble of solutions, and thus represent inferences drawn from the data. We employ statistical decision theory to find more representative estimators, centroid estimators, in a general high-dimensional discrete setting by using a family of loss functions with penalties that increase with the number of differences in components. We show that centroid estimates are obtained by maximizing the marginal probabilities of the solution components for unconstrained ensembles and for an important class of problems, including sequence alignment and the prediction of RNA secondary structure, whose ensembles contain exclusivity constraints. Three genomics examples are described that show that these estimators substantially improve predictions of ground-truth reference sets.
journal_name
Proc Natl Acad Sci U S Aauthors
Carvalho LE,Lawrence CEdoi
10.1073/pnas.0712329105subject
Has Abstractpub_date
2008-03-04 00:00:00pages
3209-14issue
9eissn
0027-8424issn
1091-6490pii
0712329105journal_volume
105pub_type
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