Predicting Genetic Regulatory Response Using Classification

We present a novel classification-based method for learning to predict gene regulatory response. Our approach is motivated by the hypothesis that in simple organisms such as Saccharomyces cerevisiae, we can learn a decision rule for predicting whether a gene is up- or down-regulated in a particular experiment based on (1) the presence of binding site subsequences (``motifs'') in the gene's regulatory region and (2) the expression levels of regulators such as transcription factors in the experiment (``parents''). Thus our learning task integrates two qualitatively different data sources: genome-wide cDNA microarray data across multiple perturbation and mutant experiments along with motif profile data from regulatory sequences. We convert the regression task of predicting real-valued gene expression measurement to a classification task of predicting +1 and -1 labels, corresponding to up- and down-regulation beyond the levels of biological and measurement noise in microarray measurements. The learning algorithm employed is boosting with a margin-based generalization of decision trees, alternating decision trees. This large-margin classifier is sufficiently flexible to allow complex logical functions, yet sufficiently simple to give insight into the combinatorial mechanisms of gene regulation. We observe encouraging prediction accuracy on experiments based on the Gasch S. cerevisiae dataset, and we show that we can accurately predict up- and down-regulation on held-out experiments. Our method thus provides predictive hypotheses, suggests biological experiments, and provides interpretable insight into the structure of genetic regulatory networks.Comment: 8 pages, 4 figures, presented at Twelfth International Conference on Intelligent Systems for Molecular Biology (ISMB 2004), supplemental website: http://www.cs.columbia.edu/compbio/geneclas

Popular Ensemble Methods: An Empirical Study

An ensemble consists of a set of individually trained classifiers (such as neural networks or decision trees) whose predictions are combined when classifying novel instances. Previous research has shown that an ensemble is often more accurate than any of the single classifiers in the ensemble. Bagging (Breiman, 1996c) and Boosting (Freund and Shapire, 1996; Shapire, 1990) are two relatively new but popular methods for producing ensembles. In this paper we evaluate these methods on 23 data sets using both neural networks and decision trees as our classification algorithm. Our results clearly indicate a number of conclusions. First, while Bagging is almost always more accurate than a single classifier, it is sometimes much less accurate than Boosting. On the other hand, Boosting can create ensembles that are less accurate than a single classifier -- especially when using neural networks. Analysis indicates that the performance of the Boosting methods is dependent on the characteristics of the data set being examined. In fact, further results show that Boosting ensembles may overfit noisy data sets, thus decreasing its performance. Finally, consistent with previous studies, our work suggests that most of the gain in an ensemble's performance comes in the first few classifiers combined; however, relatively large gains can be seen up to 25 classifiers when Boosting decision trees

On PAC-Bayesian Bounds for Random Forests

Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various PAC-Bayesian approaches to derive such bounds. The bounds do not require additional hold-out data, because the out-of-bag samples from the bagging in the training process can be exploited. A random forest predicts by taking a majority vote of an ensemble of decision trees. The first approach is to bound the error of the vote by twice the error of the corresponding Gibbs classifier (classifying with a single member of the ensemble selected at random). However, this approach does not take into account the effect of averaging out of errors of individual classifiers when taking the majority vote. This effect provides a significant boost in performance when the errors are independent or negatively correlated, but when the correlations are strong the advantage from taking the majority vote is small. The second approach based on PAC-Bayesian C-bounds takes dependencies between ensemble members into account, but it requires estimating correlations between the errors of the individual classifiers. When the correlations are high or the estimation is poor, the bounds degrade. In our experiments, we compute generalization bounds for random forests on various benchmark data sets. Because the individual decision trees already perform well, their predictions are highly correlated and the C-bounds do not lead to satisfactory results. For the same reason, the bounds based on the analysis of Gibbs classifiers are typically superior and often reasonably tight. Bounds based on a validation set coming at the cost of a smaller training set gave better performance guarantees, but worse performance in most experiments