Centroid estimation in discrete high-dimensional spaces with applications in biology.

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.

authors

Carvalho LE,Lawrence CE

doi

10.1073/pnas.0712329105

subject

Has Abstract

pub_date

2008-03-04 00:00:00

pages

3209-14

issue

9

eissn

0027-8424

issn

1091-6490

pii

0712329105

journal_volume

105

pub_type

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