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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:0016023) is a Cytoplasmic vesicle (GO:0031410) 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 SVM/AL 1 Probability 1 Data 2 SVM/AL 2 Probability 2 Data 3 SVM/AL 3 Probability 3 Data 4 SVM/AL 4 Probability 4 Data 5 SVM/AL 5 Data 6 SVM/AL 6 Data 7 SVM/AL 7 Data 8 SVM/AL 8 Probability 8 Data 33 SVM/AL 33 Probability 33 Gaussian Product, plus Bayes’ rule Probability Probability 6 Asymmetric Laplace SVM → logistic regression Data 1 SVM 1 Predict 1 Data 2 SVM 2 Predict 2 Data 3 SVM 3 Predict 3 Data 4 SVM 4 Predict 4 Data 5 SVM 5 Data 6 SVM 6 Data 7 SVM 7 Data 8 SVM 8 Predict 8 Data 33 SVM 33 Predict 33 Logistic regressor 1 Logistic regressor 2 Logistic regressor 3 Predict 6 Logistic regressor 11 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. pi max pˆ j • And: Report the product of probabilities of all ancestors and self. pi pˆ j • Or: Compute the probability that at least one descendant of the GO term is “on,” assuming independence. jDi jAi pi 1 1 pˆ j jDi • All three methods use probabilities estimated by logistic regression. Bayesian network • Belief propagation on a graphical model with the topology of the GO. • Given Yi, the distribution of each SVM output Xi 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: pi p j jAi 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. min p pˆ 2 pi , iI s.t. iI i i p j pi , i, j E 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. 2 ˆ p p min i i pi , iI s.t. iI p j pi , i, j E min D pˆ p pi , iI s.t. iI i i p j pi , i, j E 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. Hybrid method KLP BPAL BPLR Likelihood ratios obtained from logistic regression • Replace the Bayesian log posterior for Yi by the marginal log posterior obtained from the logistic regression. • Uses discriminative posteriors from logistic regression, but still uses a structural prior. Axes of evaluation • Ontology – biological process – cellular compartment – molecular function • Term size – – – – 3-10 proteins 11-30 proteins 31-100 proteins 100-200 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 Joint evaluation Precision TP/(TP+FP) Biological process ontology Large terms (101-200) Recall TP / (TP+FN) 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 KüllbackLeibler 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 3-10 953 proteins 11-30 435 proteins 31-100 239 proteins 101-200 100 proteins Biological process 3-10 476 proteins 11-30 142 proteins 31-100 111 proteins 101-200 35 proteins Molecular function 3-10 196 proteins 11-30 135 proteins 31-100 171 proteins 101-200 278 proteins Cellular component 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 3-10 953 terms 11-30 435 terms 31-100 239 terms 101-200 100 terms Biological process 3-10 476 terms 11-30 142 terms 31-100 111 terms 101-200 35 terms Molecular function 3-10 152 terms 11-30 97 terms 31-100 48 terms 101-200 30 terms Cellular component 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 Michael Jordan Gert Lanckriet 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