2,356 research outputs found
Iterative Random Forests to detect predictive and stable high-order interactions
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
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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