43,970 research outputs found
Parametric Alignment of Drosophila Genomes
The classic algorithms of Needleman--Wunsch and Smith--Waterman find a
maximum a posteriori probability alignment for a pair hidden Markov model
(PHMM). In order to process large genomes that have undergone complex genome
rearrangements, almost all existing whole genome alignment methods apply fast
heuristics to divide genomes into small pieces which are suitable for
Needleman--Wunsch alignment. In these alignment methods, it is standard
practice to fix the parameters and to produce a single alignment for subsequent
analysis by biologists.
Our main result is the construction of a whole genome parametric alignment of
Drosophila melanogaster and Drosophila pseudoobscura. Parametric alignment
resolves the issue of robustness to changes in parameters by finding all
optimal alignments for all possible parameters in a PHMM. Our alignment draws
on existing heuristics for dividing whole genomes into small pieces for
alignment, and it relies on advances we have made in computing convex polytopes
that allow us to parametrically align non-coding regions using biologically
realistic models. We demonstrate the utility of our parametric alignment for
biological inference by showing that cis-regulatory elements are more conserved
between Drosophila melanogaster and Drosophila pseudoobscura than previously
thought. We also show how whole genome parametric alignment can be used to
quantitatively assess the dependence of branch length estimates on alignment
parameters.
The alignment polytopes, software, and supplementary material can be
downloaded at http://bio.math.berkeley.edu/parametric/.Comment: 19 pages, 3 figure
Skewed Factor Models Using Selection Mechanisms
Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skew-t, and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models using the classic open/closed book exam scores dataset
Parametric Inference for Biological Sequence Analysis
One of the major successes in computational biology has been the unification,
using the graphical model formalism, of a multitude of algorithms for
annotating and comparing biological sequences. Graphical models that have been
applied towards these problems include hidden Markov models for annotation,
tree models for phylogenetics, and pair hidden Markov models for alignment. A
single algorithm, the sum-product algorithm, solves many of the inference
problems associated with different statistical models. This paper introduces
the \emph{polytope propagation algorithm} for computing the Newton polytope of
an observation from a graphical model. This algorithm is a geometric version of
the sum-product algorithm and is used to analyze the parametric behavior of
maximum a posteriori inference calculations for graphical models.Comment: 15 pages, 4 figures. See also companion paper "Tropical Geometry of
Statistical Models" (q-bio.QM/0311009
Distribution on Warp Maps for Alignment of Open and Closed Curves
Alignment of curve data is an integral part of their statistical analysis,
and can be achieved using model- or optimization-based approaches. The
parameter space is usually the set of monotone, continuous warp maps of a
domain. Infinite-dimensional nature of the parameter space encourages sampling
based approaches, which require a distribution on the set of warp maps.
Moreover, the distribution should also enable sampling in the presence of
important landmark information on the curves which constrain the warp maps. For
alignment of closed and open curves in , possibly with
landmark information, we provide a constructive, point-process based definition
of a distribution on the set of warp maps of and the unit circle
that is (1) simple to sample from, and (2) possesses the
desiderata for decomposition of the alignment problem with landmark constraints
into multiple unconstrained ones. For warp maps on , the distribution is
related to the Dirichlet process. We demonstrate its utility by using it as a
prior distribution on warp maps in a Bayesian model for alignment of two
univariate curves, and as a proposal distribution in a stochastic algorithm
that optimizes a suitable alignment functional for higher-dimensional curves.
Several examples from simulated and real datasets are provided
Inference with Constrained Hidden Markov Models in PRISM
A Hidden Markov Model (HMM) is a common statistical model which is widely
used for analysis of biological sequence data and other sequential phenomena.
In the present paper we show how HMMs can be extended with side-constraints and
present constraint solving techniques for efficient inference. Defining HMMs
with side-constraints in Constraint Logic Programming have advantages in terms
of more compact expression and pruning opportunities during inference.
We present a PRISM-based framework for extending HMMs with side-constraints
and show how well-known constraints such as cardinality and all different are
integrated. We experimentally validate our approach on the biologically
motivated problem of global pairwise alignment
MonoPerfCap: Human Performance Capture from Monocular Video
We present the first marker-less approach for temporally coherent 3D
performance capture of a human with general clothing from monocular video. Our
approach reconstructs articulated human skeleton motion as well as medium-scale
non-rigid surface deformations in general scenes. Human performance capture is
a challenging problem due to the large range of articulation, potentially fast
motion, and considerable non-rigid deformations, even from multi-view data.
Reconstruction from monocular video alone is drastically more challenging,
since strong occlusions and the inherent depth ambiguity lead to a highly
ill-posed reconstruction problem. We tackle these challenges by a novel
approach that employs sparse 2D and 3D human pose detections from a
convolutional neural network using a batch-based pose estimation strategy.
Joint recovery of per-batch motion allows to resolve the ambiguities of the
monocular reconstruction problem based on a low dimensional trajectory
subspace. In addition, we propose refinement of the surface geometry based on
fully automatically extracted silhouettes to enable medium-scale non-rigid
alignment. We demonstrate state-of-the-art performance capture results that
enable exciting applications such as video editing and free viewpoint video,
previously infeasible from monocular video. Our qualitative and quantitative
evaluation demonstrates that our approach significantly outperforms previous
monocular methods in terms of accuracy, robustness and scene complexity that
can be handled.Comment: Accepted to ACM TOG 2018, to be presented on SIGGRAPH 201
- …