We present a new algorithm for Bayesian network structure learning, called Max-Min Hill-Climbing (MMHC). The algorithm combines ideas from local learning, constraint-based, and search-and-score techniques in a principled and effective way. It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. In our extensive empirical evaluation MMHC outperforms on average and in terms of various metrics several prototypical and state-of-the-art algorithms, namely the PC, Sparse Candidate, Three Phase Dependency Analysis, Optimal Reinsertion, Greedy Equivalence Search, and Greedy Search. These are the first empirical results simultaneously comparing most of the major Bayesian network algorithms against each other. MMHC offers certain theoretical advantages, specifically over the Sparse Candidate algorithm, corroborated by our experiments. MMHC and detailed results of our study are publicly available at http://www.dsl-lab.org/supplements/mmhc paper/mmhc index.html.

alexander.statnikov@vanderbilt.edu.

BackgroundCancer diagnosis and clinical outcome prediction are among the most important emerging applications of gene expression microarray technology with several molecular signatures on their way toward clinical deployment. Use of the most accurate classification algorithms available for microarray gene expression data is a critical ingredient in order to develop the best possible molecular signatures for patient care. As suggested by a large body of literature to date, support vector machines can be considered "best of class" algorithms for classification of such data. Recent work, however, suggests that random forest classifiers may outperform support vector machines in this domain.ResultsIn the present paper we identify methodological biases of prior work comparing random forests and support vector machines and conduct a new rigorous evaluation of the two algorithms that corrects these limitations. Our experiments use 22 diagnostic and prognostic datasets and show that support vector machines outperform random forests, often by a large margin. Our data also underlines the importance of sound research design in benchmarking and comparison of bioinformatics algorithms.ConclusionWe found that both on average and in the majority of microarray datasets, random forests are outperformed by support vector machines both in the settings when no gene selection is performed and when several popular gene selection methods are used.

Data Mining with Bayesian Network learning has two important characteristics: under broad conditions learned edges between variables correspond to causal influences, and second, for every variable T in the network a special subset (Markov Blanket) identifiable by the network is the minimal variable set required to predict T . However, all known algorithms learning a complete BN do not scale up beyond a few hundred variables. On the other hand, all known sound algorithms learning a local region of the network require an exponential number of training instances to the size of the learned region.The contribution of this paper is two-fold. We introduce a novel local algorithm that returns all variables with direct edges to and from a target variable T as well as a local algorithm that returns the Markov Blanket of T . Both algorithms (i) are sound, (ii) can be run efficiently in datasets with thousands of variables, and (iii) significantly outperform in terms of approximating the true neighborhood previous state-of-the-art algorithms using only a fraction of the training size required by the existing methods. A fundamental difference between our approach and existing ones is that the required sample depends on the generating graph connectivity and not the size of the local region; this yields up to exponential savings in sample relative to previously known algorithms. The results presented here are promising not only for discovery of local causal structure, and variable selection for classification, but also for the induction of complete BNs.

BackgroundRecent advances in next-generation DNA sequencing enable rapid high-throughput quantitation of microbial community composition in human samples, opening up a new field of microbiomics. One of the promises of this field is linking abundances of microbial taxa to phenotypic and physiological states, which can inform development of new diagnostic, personalized medicine, and forensic modalities. Prior research has demonstrated the feasibility of applying machine learning methods to perform body site and subject classification with microbiomic data. However, it is currently unknown which classifiers perform best among the many available alternatives for classification with microbiomic data.ResultsIn this work, we performed a systematic comparison of 18 major classification methods, 5 feature selection methods, and 2 accuracy metrics using 8 datasets spanning 1,802 human samples and various classification tasks: body site and subject classification and diagnosis.ConclusionsWe found that random forests, support vector machines, kernel ridge regression, and Bayesian logistic regression with Laplace priors are the most effective machine learning techniques for performing accurate classification from these microbiomic data.