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. 2013 Jul 1;29(13):i53-61.
doi: 10.1093/bioinformatics/btt228.

Information-theoretic Evaluation of Predicted Ontological Annotations

Free PMC article

Information-theoretic Evaluation of Predicted Ontological Annotations

Wyatt T Clark et al. Bioinformatics. .
Free PMC article


Motivation: The development of effective methods for the prediction of ontological annotations is an important goal in computational biology, with protein function prediction and disease gene prioritization gaining wide recognition. Although various algorithms have been proposed for these tasks, evaluating their performance is difficult owing to problems caused both by the structure of biomedical ontologies and biased or incomplete experimental annotations of genes and gene products.

Results: We propose an information-theoretic framework to evaluate the performance of computational protein function prediction. We use a Bayesian network, structured according to the underlying ontology, to model the prior probability of a protein's function. We then define two concepts, misinformation and remaining uncertainty, that can be seen as information-theoretic analogs of precision and recall. Finally, we propose a single statistic, referred to as semantic distance, that can be used to rank classification models. We evaluate our approach by analyzing the performance of three protein function predictors of Gene Ontology terms and provide evidence that it addresses several weaknesses of currently used metrics. We believe this framework provides useful insights into the performance of protein function prediction tools.

Supplementary information: Supplementary data are available at Bioinformatics online.


Fig. 1.
Fig. 1.
An example of an ontology, dataset and calculation of information content. (A) An ontology viewed as a Bayesian network together with a conditional probability table assigned to each node. Each conditional probability table is limited to a single number owing to the consistency requirement in assignments of protein function. Information accretion calculated for each node, e.g. formula image, are shown in gray next to each node. (B) A dataset containing four proteins whose functional annotations are generated according to the probability distribution from the Bayesian network. (C) The total information content associated with each protein found in panel (B); e.g. formula image formula image. Note that formula image and formula image, although proteins with such annotation have not been observed in part (B)
Fig. 2.
Fig. 2.
Illustration of calculating remaining uncertainty and misinformation, given a predicted annotation graph P and a graph of true annotations T. Graphs P and T are uniquely determined by the leaf nodes p1, p2, t1, and t2, respectively. Nodes colored in gray represent graph T. Nodes circled in gray are used to determine remaining uncertainty (ru; right side) and misinformation (mi; left side) between T and P
Fig. 3.
Fig. 3.
Distribution of information content (in bits) over proteins annotated by terms for each of the three ontologies. The average information content of a protein was estimated at 10.9 (std. 10.2), 32.0 (std. 33.6) and 10.4 (std. 9.2) bits for MFO, BPO and CCO, respectively
Fig. 4.
Fig. 4.
The 2D evaluation plots. Each plot shows three prediction methods: Naive (gray, dashed), BLAST (red, solid) and GOtcha (blue, solid) constructed using cross-validation. Green point labeled GO shows the performance evaluation between two databases of experimental annotations, downloaded at the same time. The rows show the performance for different ontologies (MFO, BPO, CCO). The columns show different evaluation metrics: formula image and formula image

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    1. Alterovitz G, et al. Ontology engineering. Nat. Biotechnol. 2010;28:128–130. - PMC - PubMed
    1. Altschul SF, et al. Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res. 1997;25:3389–3402. - PMC - PubMed
    1. Ashburner M, et al. Gene ontology: tool for the unification of biology. The gene ontology consortium. Nat. Genet. 2000;25:25–29. - PMC - PubMed
    1. Clark WT, Radivojac P. Analysis of protein function and its prediction from amino acid sequence. Proteins. 2011;79:2086–2096. - PubMed
    1. Guzzi PH, et al. Semantic similarity analysis of protein data: assessment with biological features and issues. Brief. Bioinform. 2012;13:569–585. - PubMed

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