2,356 research outputs found

    Iterative Random Forests to detect predictive and stable high-order interactions

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    Genomics has revolutionized biology, enabling the interrogation of whole transcriptomes, genome-wide binding sites for proteins, and many other molecular processes. However, individual genomic assays measure elements that interact in vivo as components of larger molecular machines. Understanding how these high-order interactions drive gene expression presents a substantial statistical challenge. Building on Random Forests (RF), Random Intersection Trees (RITs), and through extensive, biologically inspired simulations, we developed the iterative Random Forest algorithm (iRF). iRF trains a feature-weighted ensemble of decision trees to detect stable, high-order interactions with same order of computational cost as RF. We demonstrate the utility of iRF for high-order interaction discovery in two prediction problems: enhancer activity in the early Drosophila embryo and alternative splicing of primary transcripts in human derived cell lines. In Drosophila, among the 20 pairwise transcription factor interactions iRF identifies as stable (returned in more than half of bootstrap replicates), 80% have been previously reported as physical interactions. Moreover, novel third-order interactions, e.g. between Zelda (Zld), Giant (Gt), and Twist (Twi), suggest high-order relationships that are candidates for follow-up experiments. In human-derived cells, iRF re-discovered a central role of H3K36me3 in chromatin-mediated splicing regulation, and identified novel 5th and 6th order interactions, indicative of multi-valent nucleosomes with specific roles in splicing regulation. By decoupling the order of interactions from the computational cost of identification, iRF opens new avenues of inquiry into the molecular mechanisms underlying genome biology

    Regular configurations and TBR graphs

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    PhD 2009 QMThis thesis consists of two parts: The first one is concerned with the theory and applications of regular configurations; the second one is devoted to TBR graphs. In the first part, a new approach is proposed to study regular configurations, an extremal arrangement of necklaces formed by a given number of red beads and black beads. We first show that this concept is closely related to several other concepts studied in the literature, such as balanced words, maximally even sets, and the ground states in the Kawasaki-Ising model. Then we apply regular configurations to solve the (vertex) cycle packing problem for shift digraphs, a family of Cayley digraphs. TBR is one of widely used tree rearrangement operationes, and plays an important role in heuristic algorithms for phylogenetic tree reconstruction. In the second part of this thesis we study various properties of TBR graphs, a family of graphs associated with the TBR operation. To investigate the degree distribution of the TBR graphs, we also study -index, a concept introduced to measure the shape of trees. As an interesting by-product, we obtain a structural characterization of good trees, a well-known family of trees that generalizes the complete binary trees
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