We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis.
A number of probabilistic approaches have been proposed in the past for the problem of gene-regulatory network reconstruction @cite_10 @cite_13 @cite_4 @cite_3 . Some take into account the information on the prior network topology @cite_10 , which is not always available. Most assume the number of factors is known. To get around this, one can perform model selection via Reversible Jump MCMC @cite_0 or evolutionary stochastic model search @cite_12 . Unfortunately, these methods are often difficult to design and may take quite long to converge. Moreover, they are difficult to integrate with other forms of prior knowledge (eg., factor hierarchies). A somewhat similar approach to ours is the infinite independent component analysis (iICA) model of @cite_8 which treats factor analysis as a special case of ICA. However, their model is limited to factor analysis and does not take into account feature selection, factor hierarchy and factor regression. As a generalization to the standard ICA model, @cite_11 proposed a model in which the components can be related via a tree-structured graphical model. It, however, assumes a fixed number of components.
@cite_4 @cite_8 @cite_10 @cite_3 @cite_0 @cite_13 @cite_12 @cite_11
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We consider the problem of discovering gene regulatory networks from time-series microarray data. Recently, graphical Granger modeling has gained considerable attention as a promising direction for addressing this problem. These methods apply graphical modeling methods on time-series data and invoke the notion of ‘Granger causality’ to make assertions on causality through inference on time-lagged effects. Existing algorithms, however, have neglected an important aspect of the problem—the group structure among the lagged temporal variables naturally imposed by the time series they belong to. Specifically, existing methods in computational biology share this shortcoming, as well as additional computational limitations, prohibiting their effective applications to the large datasets including a large number of genes and many data points. In the present article, we propose a novel methodology which we term ‘grouped graphical Granger modeling method’, which overcomes the limitations mentioned above by applying a regression method suited for high-dimensional and large data, and by leveraging the group structure among the lagged temporal variables according to the time series they belong to. We demonstrate the effectiveness of the proposed methodology on both simulated and actual gene expression data, specifically the human cancer cell (HeLa S3) cycle data. The simulation results show that the proposed methodology generally exhibits higher accuracy in recovering the underlying causal structure. Those on the gene expression data demonstrate that it leads to improved accuracy with respect to prediction of known links, and also uncovers additional causal relationships uncaptured by earlier works. Contact: aclozano@us.ibm.com The identification of probabilistic cellular automata (PCA) is studied using a new two stage neighborhood detection algorithm. It is shown that a binary probabilistic cellular automaton (BPCA) can be described by an integer-parameterized polynomial corrupted by noise. Searching for the correct neighborhood of a BPCA is then equivalent to selecting the correct terms which constitute the polynomial model of the BPCA, from a large initial term set. It is proved that the contribution values for the correct terms can be calculated independently of the contribution values for the noise terms. This allows the neighborhood detection technique developed for deterministic rules in to be applied with a larger cutoff value to discard the majority of spurious terms and to produce an initial presearch for the BPCA neighborhood. A multiobjective genetic algorithm (GA) search with integer constraints is then evolved to refine the reduced neighborhood and to identify the polynomial rule which is equivalent to the probabilistic rule with the largest probability. A probability table representing the BPCA can then be determined based on the identified neighborhood and the deterministic rule. The new algorithm is tested over a large set of one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) BPCA rules. Simulation results demonstrate the efficiency of the new method. Objective Build probabilistic topic model representations of hospital admissions processes and compare the ability of such models to predict clinical order patterns as compared to preconstructed order sets. @PARASPLIT Materials and Methods The authors evaluated the first 24 hours of structured electronic health record data for > 10 K inpatients. Drawing an analogy between structured items (e.g., clinical orders) to words in a text document, the authors performed latent Dirichlet allocation probabilistic topic modeling. These topic models use initial clinical information to predict clinical orders for a separate validation set of > 4 K patients. The authors evaluated these topic model-based predictions vs existing human-authored order sets by area under the receiver operating characteristic curve, precision, and recall for subsequent clinical orders. @PARASPLIT Results Existing order sets predict clinical orders used within 24 hours with area under the receiver operating characteristic curve 0.81, precision 16 , and recall 35 . This can be improved to 0.90, 24 , and 47 ( P < 10−20) by using probabilistic topic models to summarize clinical data into up to 32 topics. Many of these latent topics yield natural clinical interpretations (e.g., “critical care,” “pneumonia,” “neurologic evaluation”). @PARASPLIT Discussion Existing order sets tend to provide nonspecific, process-oriented aid, with usability limitations impairing more precise, patient-focused support. Algorithmic summarization has the potential to breach this usability barrier by automatically inferring patient context, but with potential tradeoffs in interpretability. @PARASPLIT Conclusion Probabilistic topic modeling provides an automated approach to detect thematic trends in patient care and generate decision support content. A potential use case finds related clinical orders for decision support. Motivation: Approaches for testing sets of variants, such as a set of rare or common variants within a gene or pathway, for association with complex traits are important. In particular, set tests allow for aggregation of weak signal within a set, can capture interplay among variants and reduce the burden of multiple hypothesis testing. Until now, these approaches did not address confounding by family relatedness and population structure, a problem that is becoming more important as larger datasets are used to increase power. Results: We introduce a new approach for set tests that handles confounders. Our model is based on the linear mixed model and uses two random effects—one to capture the set association signal and one to capture confounders. We also introduce a computational speedup for two random-effects models that makes this approach feasible even for extremely large cohorts. Using this model with both the likelihood ratio test and score test, we find that the former yields more power while controlling type I error. Application of our approach to richly structured Genetic Analysis Workshop 14 data demonstrates that our method successfully corrects for population structure and family relatedness, whereas application of our method to a 15 000 individual Crohn’s disease case–control cohort demonstrates that it additionally recovers genes not recoverable by univariate analysis. Availability: A Python-based library implementing our approach is available at http: mscompbio.codeplex.com. Contact:jennl@microsoft.com or lippert@microsoft.com or heckerma@microsoft.com Supplementary information:Supplementary data are available at Bioinformatics online.