Consistent probabilistic outputs for protein function prediction William Stafford Noble Department of Genome Sciences Department of Computer Science and Engineering University of Washington

Outline Motivation and background Methods –Shared base method –Reconciliation methods Results

The problem Given: protein sequence, knockout phenotype, gene expression profile, protein-protein interactions, and phylogenetic profile Predict a probability for every term in the Gene Ontology  Heterogeneous data  Missing data  Multiple labels per gene  Structured output

Consistent predictions Cytoplasmic membrane-bound vesicle (GO: ) Cytoplasmic vesicle (GO: ) is a The probability that protein X is a cytoplasmic membrane-bound vesicle must be less than or equal to the probability that protein X is a cytoplasmic vesicle.

Data sets

Kernels

SVM → Naïve Bayes Data 1 Data 2 Data 3 Data 4 Data 5 Data 6 Data 7 Data 8 Data 33 SVM/AL 1 SVM/AL 2 SVM/AL 3 SVM/AL 4 SVM/AL 5 SVM/AL 6 SVM/AL 7 SVM/AL 8 SVM/AL 33 Product, plus Bayes’ rule Probability 1 Probability 2 Probability 3 Probability 4 Probability 6 Probability 8 Probability 33 Probability Gaussian Asymmetric Laplace

SVM → logistic regression Data 1 Data 2 Data 3 Data 4 Data 5 Data 6 Data 7 Data 8 Data 33 SVM 1 SVM 2 SVM 3 SVM 4 SVM 5 SVM 6 SVM 7 SVM 8 SVM 33 Logistic regressor 1 Logistic regressor 2 Logistic regressor 3 Logistic regressor 11 Predict 1 Predict 2 Predict 3 Predict 4 Predict 6 Predict 8 Predict 33 Probability

Reconciliation Methods 3 heuristic methods 3 Bayesian networks 1 cascaded logistic regression 3 projection methods

Heuristic methods Max: Report the maximum probability of self and all descendants. And: Report the product of probabilities of all ancestors and self. Or: Compute the probability that at least one descendant of the GO term is “on,” assuming independence. All three methods use probabilities estimated by logistic regression.

Bayesian network Belief propagation on a graphical model with the topology of the GO. Given Y i, the distribution of each SVM output X i is modeled as an independent asymmetric Laplace distribution. Solved using a variational inference algorithm. “Flipped” variant: reverse the directionality of edges in the graph.

Cascaded logistic regression Fit a logistic regression to the SVM output only for those proteins that belong to all parent terms. Models the conditional distribution of the term, given all parents. The final probability is the product of these conditionals:

Isotonic regression Consider the squared Euclidean distance between two sets of probabilities. Find the closest set of probabilities to the logistic regression values that satisfy all the inequality constraints.

Isotonic regression Consider the squared Euclidean distance between two sets of probabilities. Find the closest set of probabilities to the logistic regression values that satisfy all the inequality constraints.

Küllback-Leibler projection Küllback-Leibler projection on the set of distributions which factorize according to the ontology graph. Two variants, depending on the directions of the edges.

Likelihood ratios obtained from logistic regression Hybrid method Replace the Bayesian log posterior for Y i by the marginal log posterior obtained from the logistic regression. Uses discriminative posteriors from logistic regression, but still uses a structural prior. BPAL KLP BPLR

Axes of evaluation Ontology –biological process –cellular compartment –molecular function Term size –3-10 proteins –11-30 proteins – proteins – proteins Evaluation mode –Joint evaluation –Per protein –Per term Recall –1% –10% –50% –80%

Legend Belief propagation, asymmetric Laplace Belief propagation, asymmetric Laplace, flipped Belief propagation, logistic regression Cascaded logistic regression Isotonic regression Logistic regression Küllback-Leibler projection Küllback-Leibler projection, flipped Naïve Bayes, asymmetric Laplace

Precision TP/(TP+FP) Recall TP / (TP+FN) Joint evaluation Biological process ontology Large terms ( )

Biological process ontology

Molecular function ontology

Cellular compartment ontology

Conclusions: Joint evaluation Reconciliation does not always help. Isotonic regression performs well overall, especially for recall > 20%. For lower recall values, both Küllback- Leibler projection methods work well.

Average precision per protein Biological process All term sizes

Biological process

Statistical significance Biological process Large terms

Biological process Large terms

Biological process proteins 435 proteins 239 proteins 100 proteins

Molecular function proteins 142 proteins 111 proteins 35 proteins

Cellular component proteins 135 proteins 171 proteins 278 proteins

Conclusions: per protein Several methods perform well –Unreconciled logistic regression –Unreconciled naïve Bayes –Isotonic regression –Belief propagation with asymmetric Laplace For small terms –For molecular function and biological process, we do not observe many significant differences. –For cellular components, belief propagation with logistic regression works well.

Average precision per term Biological process All term sizes

Biological process terms 435 terms 239 terms 100 terms

Molecular function terms 142 terms 111 terms 35 terms

Cellular component terms 97 terms 48 terms 30 terms

Conclusions Reconciliation does not always help. Isotonic regression (IR) performs well overall. For small biological process and molecular function terms, it is less clear that IR is one of the best methods.

Acknowledgments Guillaume Obozinski Charles Grant Gert Lanckriet Michael Jordan The mousefunc organizers Tim Hughes Lourdes Pena-Castillo Fritz Roth Gabriel Berriz Frank Gibbons

Per term for small terms Biological process Molecular function Cellular component