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.

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.

No abstract

The number of microbiome-related studies has notably increased the availability of data on human microbiome composition and function. These studies provide the essential material to deeply explore host-microbiome associations and their relation to the development and progression of various complex diseases. Improved data-analytical tools are needed to exploit all information from these biological datasets, taking into account the peculiarities of microbiome data, i.e., compositional, heterogeneous and sparse nature of these datasets. The possibility of predicting host-phenotypes based on taxonomy-informed feature selection to establish an association between microbiome and predict disease states is beneficial for personalized medicine. In this regard, machine learning (ML) provides new insights into the development of models that can be used to predict outputs, such as classification and prediction in microbiology, infer host phenotypes to predict diseases and use microbial communities to stratify patients by their characterization of state-specific microbial signatures. Here we review the state-of-the-art ML methods and respective software applied in human microbiome studies, performed as part of the COST Action ML4Microbiome activities. This scoping review focuses on the application of ML in microbiome studies related to association and clinical use for diagnostics, prognostics, and therapeutics. Although the data presented here is more related to the bacterial community, many algorithms could be applied in general, regardless of the feature type. This literature and software review covering this broad topic is aligned with the scoping review methodology. The manual identification of data sources has been complemented with: (1) automated publication search through digital libraries of the three major publishers using natural language processing (NLP) Toolkit, and (2) an automated identification of relevant software repositories on GitHub and ranking of the related research papers relying on learning to rank approach.