Motivation: As an increasing number of genome-wide association studies reveal the limitations of the attempt to explain phenotypic heritability by single genetic loci, there is a recent focus on associating complex phenotypes with sets of genetic loci. Although several methods for multi-locus mapping have been proposed, it is often unclear how to relate the detected loci to the growing knowledge about gene pathways and networks. The few methods that take biological pathways or networks into account are either restricted to investigating a limited number of predetermined sets of loci or do not scale to genome-wide settings.Results: We present SConES, a new efficient method to discover sets of genetic loci that are maximally associated with a phenotype while being connected in an underlying network. Our approach is based on a minimum cut reformulation of the problem of selecting features under sparsity and connectivity constraints, which can be solved exactly and rapidly.SConES outperforms state-of-the-art competitors in terms of runtime, scales to hundreds of thousands of genetic loci and exhibits higher power in detecting causal SNPs in simulation studies than other methods. On flowering time phenotypes and genotypes from Arabidopsis thaliana, SConES detects loci that enable accurate phenotype prediction and that are supported by the literature.Availability: Code is available at http://webdav.tuebingen.mpg.de/u/karsten/Forschung/scones/.Contact: chloe-agathe.azencott@tuebingen.mpg.deSupplementary information: Supplementary data are available at Bioinformatics online.

We use artificial neural networks (ANNs) based on the Boltzmann machine (BM) architectures as an encoder of ab initio molecular many-electron wave functions represented with the complete active space configuration interaction (CAS-CI) model. As first introduced by the work of Carleo and Troyer for physical systems, the coefficients of the electronic configurations in the CI expansion are parametrized with the BMs as a function of their occupancies that act as descriptors. This ANN-based wave function ansatz is referred to as the neural-network quantum state (NQS). The machine learning is used for training the BMs in terms of finding a variationally optimal form of the ground-state wave function on the basis of the energy minimization. It is relevant to reinforcement learning and does not use any reference data nor prior knowledge of the wave function, while the Hamiltonian is given based on a user-specified chemical structure in the first-principles manner. Carleo and Troyer used the restricted Boltzmann machine (RBM), which has hidden units, for the neural network architecture of NQS, while, in this study, we further introduce its replacement with the BM that has only visible units but with different orders of connectivity. For this hidden-node free BM, the second- and third-order BMs based on quadratic and cubic energy functions, respectively, were implemented. We denote these second- and third-order BMs as BM2 and BM3, respectively. The pilot implementation of the NQS solver into an exact diagonalization module of the quantum chemistry program was made to assess the capability of variants of the BM-based NQS. The test calculations were performed by determining the CAS-CI wave functions of illustrative molecular systems, indocyanine green, and dinitrogen dissociation. The simulated energies have been shown to converge to CAS-CI energy in most cases by improving RBM with an increasing number of hidden nodes. BM3 systematically yields lower energies than BM2, reproducing the CAS-CI energies of dinitrogen across potential energy curves within an error of 50 μE h.

We present a novel algorithm, Westfall-Young light, for detecting patterns, such as itemsets and subgraphs, which are statistically significantly enriched in one of two classes. Our method corrects rigorously for multiple hypothesis testing and correlations between patterns through the WestfallYoung permutation procedure, which empirically estimates the null distribution of pattern frequencies in each class via permutations.In our experiments, Westfall-Young light dramatically outperforms the current state-of-the-art approach in terms of both runtime and memory efficiency on popular real-world benchmark datasets for pattern mining. The key to this efficiency is that unlike all existing methods, our algorithm neither needs to solve the underlying frequent itemset mining problem anew for each permutation nor needs to store the occurrence list of all frequent patterns. Westfall-Young light opens the door to significant pattern mining on large datasets that previously led to prohibitive runtime or memory costs.

Motivation: Genetic heterogeneity, the fact that several sequence variants give rise to the same phenotype, is a phenomenon that is of the utmost interest in the analysis of complex phenotypes. Current approaches for finding regions in the genome that exhibit genetic heterogeneity suffer from at least one of two shortcomings: (i) they require the definition of an exact interval in the genome that is to be tested for genetic heterogeneity, potentially missing intervals of high relevance, or (ii) they suffer from an enormous multiple hypothesis testing problem due to the large number of potential candidate intervals being tested, which results in either many false positives or a lack of power to detect true intervals.Results: Here, we present an approach that overcomes both problems: it allows one to automatically find all contiguous sequences of single nucleotide polymorphisms in the genome that are jointly associated with the phenotype. It also solves both the inherent computational efficiency problem and the statistical problem of multiple hypothesis testing, which are both caused by the huge number of candidate intervals. We demonstrate on Arabidopsis thaliana genome-wide association study data that our approach can discover regions that exhibit genetic heterogeneity and would be missed by single-locus mapping.Conclusions: Our novel approach can contribute to the genome-wide discovery of intervals that are involved in the genetic heterogeneity underlying complex phenotypes.Availability and implementation: The code can be obtained at: http://www.bsse.ethz.ch/mlcb/research/bioinformatics-and-computational-biology/sis.html.Contact: felipe.llinares@bsse.ethz.chSupplementary information: Supplementary data are available at Bioinformatics online.