1,775 research outputs found
Horseshoe-based Bayesian nonparametric estimation of effective population size trajectories
Phylodynamics is an area of population genetics that uses genetic sequence
data to estimate past population dynamics. Modern state-of-the-art Bayesian
nonparametric methods for recovering population size trajectories of unknown
form use either change-point models or Gaussian process priors. Change-point
models suffer from computational issues when the number of change-points is
unknown and needs to be estimated. Gaussian process-based methods lack local
adaptivity and cannot accurately recover trajectories that exhibit features
such as abrupt changes in trend or varying levels of smoothness. We propose a
novel, locally-adaptive approach to Bayesian nonparametric phylodynamic
inference that has the flexibility to accommodate a large class of functional
behaviors. Local adaptivity results from modeling the log-transformed effective
population size a priori as a horseshoe Markov random field, a recently
proposed statistical model that blends together the best properties of the
change-point and Gaussian process modeling paradigms. We use simulated data to
assess model performance, and find that our proposed method results in reduced
bias and increased precision when compared to contemporary methods. We also use
our models to reconstruct past changes in genetic diversity of human hepatitis
C virus in Egypt and to estimate population size changes of ancient and modern
steppe bison. These analyses show that our new method captures features of the
population size trajectories that were missed by the state-of-the-art methods.Comment: 36 pages, including supplementary informatio
Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields
We present \emph{telescoping} recursive representations for both continuous
and discrete indexed noncausal Gauss-Markov random fields. Our recursions start
at the boundary (a hypersurface in , ) and telescope inwards.
For example, for images, the telescoping representation reduce recursions from
to , i.e., to recursions on a single dimension. Under
appropriate conditions, the recursions for the random field are linear
stochastic differential/difference equations driven by white noise, for which
we derive recursive estimation algorithms, that extend standard algorithms,
like the Kalman-Bucy filter and the Rauch-Tung-Striebel smoother, to noncausal
Markov random fields.Comment: To appear in the Transactions on Information Theor
Arriving on time: estimating travel time distributions on large-scale road networks
Most optimal routing problems focus on minimizing travel time or distance
traveled. Oftentimes, a more useful objective is to maximize the probability of
on-time arrival, which requires statistical distributions of travel times,
rather than just mean values. We propose a method to estimate travel time
distributions on large-scale road networks, using probe vehicle data collected
from GPS. We present a framework that works with large input of data, and
scales linearly with the size of the network. Leveraging the planar topology of
the graph, the method computes efficiently the time correlations between
neighboring streets. First, raw probe vehicle traces are compressed into pairs
of travel times and number of stops for each traversed road segment using a
`stop-and-go' algorithm developed for this work. The compressed data is then
used as input for training a path travel time model, which couples a Markov
model along with a Gaussian Markov random field. Finally, scalable inference
algorithms are developed for obtaining path travel time distributions from the
composite MM-GMRF model. We illustrate the accuracy and scalability of our
model on a 505,000 road link network spanning the San Francisco Bay Area
Diffusion Adaptation Strategies for Distributed Estimation over Gaussian Markov Random Fields
The aim of this paper is to propose diffusion strategies for distributed
estimation over adaptive networks, assuming the presence of spatially
correlated measurements distributed according to a Gaussian Markov random field
(GMRF) model. The proposed methods incorporate prior information about the
statistical dependency among observations, while at the same time processing
data in real-time and in a fully decentralized manner. A detailed mean-square
analysis is carried out in order to prove stability and evaluate the
steady-state performance of the proposed strategies. Finally, we also
illustrate how the proposed techniques can be easily extended in order to
incorporate thresholding operators for sparsity recovery applications.
Numerical results show the potential advantages of using such techniques for
distributed learning in adaptive networks deployed over GMRF.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin
note: text overlap with arXiv:1206.309
Unsupervised Texture Segmentation using Active Contours and Local Distributions of Gaussian Markov Random Field Parameters
In this paper, local distributions of low order Gaussian Markov Random Field (GMRF) model parameters are proposed as texture features for unsupervised texture segmentation.Instead of using model parameters as texture features, we exploit the variations in parameter estimates found by model fitting in local region around the given pixel. Thespatially localized estimation process is carried out by maximum likelihood method employing a moderately small estimation window which leads to modeling of partial texturecharacteristics belonging to the local region. Hence significant fluctuations occur in the estimates which can be related to texture pattern complexity. The variations occurred in estimates are quantified by normalized local histograms. Selection of an accurate window size for histogram calculation is crucial and is achieved by a technique based on the entropy of textures. These texture features expand the possibility of using relativelylow order GMRF model parameters for segmenting fine to very large texture patterns and offer lower computational cost. Small estimation windows result in better boundarylocalization. Unsupervised segmentation is performed by integrated active contours, combining the region and boundary information. Experimental results on statistical and structural component textures show improved discriminative ability of the features compared to some recent algorithms in the literature
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