BACKGROUND: Finding a globally optimal Bayesian Network using exhaustive search is a problem with super-exponential complexity, which severely restricts the number of variables that can feasibly be included. We implement a dynamic programming based algorithm with built-in dimensionality reduction and parent set identification. This reduces the search space substantially and can be applied to large-dimensional data. We use what we call 'generational orderings' based search for optimal networks, which is a novel way to efficiently search the space of possible networks given the possible parent sets. The algorithm supports both continuous and categorical data, as well as continuous, binary and survival outcomes. RESULTS: We demonstrate the efficacy of our algorithm on both synthetic and real data. In simulations, our algorithm performs better than three state-of-art algorithms that are currently used extensively. We then apply it to an Ovarian Cancer gene expression dataset with 513 genes and a survival outcome. Our algorithm is able to find an optimal network describing the disease pathway consisting of 6 genes leading to the outcome node in just 3.4 min on a personal computer with a 2.3 GHz Intel Core i9 processor with 16 GB RAM. CONCLUSIONS: Our generational orderings based search for optimal networks is both an efficient and highly scalable approach for finding optimal Bayesian Networks and can be applied to 1000 s of variables. Using specifiable parameters-correlation, FDR cutoffs, and in-degree-one can increase or decrease the number of nodes and density of the networks. Availability of two scoring option-BIC and Bge-and implementation for survival outcomes and mixed data types makes our algorithm very suitable for many types of high dimensional data in a variety of fields.

MOTIVATION: Large amounts of information generated by genomic technologies are accompanied by statistical and computational challenges due to redundancy, badly behaved data and noise. Dimensionality reduction (DR) methods have been developed to mitigate these challenges. However, many approaches are not scalable to large dimensions or result in excessive information loss. RESULTS: The proposed approach partitions data into subsets of related features and summarizes each into one and only one new feature, thus defining a surjective mapping. A constraint on information loss determines the size of the reduced dataset. Simulation studies demonstrate that when multiple related features are associated with a response, this approach can substantially increase the number of true associations detected as compared to principal components analysis, non-negative matrix factorization or no DR. This increase in true discoveries is explained both by a reduced multiple-testing challenge and a reduction in extraneous noise. In an application to real data collected from metastatic colorectal cancer tumors, more associations between gene expression features and progression free survival and response to treatment were detected in the reduced than in the full untransformed dataset. AVAILABILITY AND IMPLEMENTATION: Freely available R package from CRAN, https://cran.r-project.org/package=partition. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The challenges of successfully applying causal inference methods include: (i) satisfying underlying assumptions, (ii) limitations in data/models accommodated by the software and (iii) low power of common multiple testing approaches. RESULTS: The causal inference test (CIT) is based on hypothesis testing rather than estimation, allowing the testable assumptions to be evaluated in the determination of statistical significance. A user-friendly software package provides P-values and optionally permutation-based FDR estimates (q-values) for potential mediators. It can handle single and multiple binary and continuous instrumental variables, binary or continuous outcome variables and adjustment covariates. Also, the permutation-based FDR option provides a non-parametric implementation. CONCLUSION: Simulation studies demonstrate the validity of the cit package and show a substantial advantage of permutation-based FDR over other common multiple testing strategies. AVAILABILITY AND IMPLEMENTATION: The cit open-source R package is freely available from the CRAN website (https://cran.r-project.org/web/packages/cit/index.html) with embedded C ++ code that utilizes the GNU Scientific Library, also freely available (http://www.gnu.org/software/gsl/). CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.