9,247 research outputs found
Bayesian Estimation of White Matter Atlas from High Angular Resolution Diffusion Imaging
We present a Bayesian probabilistic model to estimate the brain white matter
atlas from high angular resolution diffusion imaging (HARDI) data. This model
incorporates a shape prior of the white matter anatomy and the likelihood of
individual observed HARDI datasets. We first assume that the atlas is generated
from a known hyperatlas through a flow of diffeomorphisms and its shape prior
can be constructed based on the framework of large deformation diffeomorphic
metric mapping (LDDMM). LDDMM characterizes a nonlinear diffeomorphic shape
space in a linear space of initial momentum uniquely determining diffeomorphic
geodesic flows from the hyperatlas. Therefore, the shape prior of the HARDI
atlas can be modeled using a centered Gaussian random field (GRF) model of the
initial momentum. In order to construct the likelihood of observed HARDI
datasets, it is necessary to study the diffeomorphic transformation of
individual observations relative to the atlas and the probabilistic
distribution of orientation distribution functions (ODFs). To this end, we
construct the likelihood related to the transformation using the same
construction as discussed for the shape prior of the atlas. The probabilistic
distribution of ODFs is then constructed based on the ODF Riemannian manifold.
We assume that the observed ODFs are generated by an exponential map of random
tangent vectors at the deformed atlas ODF. Hence, the likelihood of the ODFs
can be modeled using a GRF of their tangent vectors in the ODF Riemannian
manifold. We solve for the maximum a posteriori using the
Expectation-Maximization algorithm and derive the corresponding update
equations. Finally, we illustrate the HARDI atlas constructed based on a
Chinese aging cohort of 94 adults and compare it with that generated by
averaging the coefficients of spherical harmonics of the ODF across subjects
Bayesian Cluster Enumeration Criterion for Unsupervised Learning
We derive a new Bayesian Information Criterion (BIC) by formulating the
problem of estimating the number of clusters in an observed data set as
maximization of the posterior probability of the candidate models. Given that
some mild assumptions are satisfied, we provide a general BIC expression for a
broad class of data distributions. This serves as a starting point when
deriving the BIC for specific distributions. Along this line, we provide a
closed-form BIC expression for multivariate Gaussian distributed variables. We
show that incorporating the data structure of the clustering problem into the
derivation of the BIC results in an expression whose penalty term is different
from that of the original BIC. We propose a two-step cluster enumeration
algorithm. First, a model-based unsupervised learning algorithm partitions the
data according to a given set of candidate models. Subsequently, the number of
clusters is determined as the one associated with the model for which the
proposed BIC is maximal. The performance of the proposed two-step algorithm is
tested using synthetic and real data sets.Comment: 14 pages, 7 figure
HodgeRank with Information Maximization for Crowdsourced Pairwise Ranking Aggregation
Recently, crowdsourcing has emerged as an effective paradigm for
human-powered large scale problem solving in various domains. However, task
requester usually has a limited amount of budget, thus it is desirable to have
a policy to wisely allocate the budget to achieve better quality. In this
paper, we study the principle of information maximization for active sampling
strategies in the framework of HodgeRank, an approach based on Hodge
Decomposition of pairwise ranking data with multiple workers. The principle
exhibits two scenarios of active sampling: Fisher information maximization that
leads to unsupervised sampling based on a sequential maximization of graph
algebraic connectivity without considering labels; and Bayesian information
maximization that selects samples with the largest information gain from prior
to posterior, which gives a supervised sampling involving the labels collected.
Experiments show that the proposed methods boost the sampling efficiency as
compared to traditional sampling schemes and are thus valuable to practical
crowdsourcing experiments.Comment: Accepted by AAAI201
Joint Transmit and Receive Filter Optimization for Sub-Nyquist Delay-Doppler Estimation
In this article, a framework is presented for the joint optimization of the
analog transmit and receive filter with respect to a parameter estimation
problem. At the receiver, conventional signal processing systems restrict the
two-sided bandwidth of the analog pre-filter to the rate of the
analog-to-digital converter to comply with the well-known Nyquist-Shannon
sampling theorem. In contrast, here we consider a transceiver that by design
violates the common paradigm . To this end, at the receiver, we
allow for a higher pre-filter bandwidth and study the achievable
parameter estimation accuracy under a fixed sampling rate when the transmit and
receive filter are jointly optimized with respect to the Bayesian
Cram\'{e}r-Rao lower bound. For the case of delay-Doppler estimation, we
propose to approximate the required Fisher information matrix and solve the
transceiver design problem by an alternating optimization algorithm. The
presented approach allows us to explore the Pareto-optimal region spanned by
transmit and receive filters which are favorable under a weighted mean squared
error criterion. We also discuss the computational complexity of the obtained
transceiver design by visualizing the resulting ambiguity function. Finally, we
verify the performance of the optimized designs by Monte-Carlo simulations of a
likelihood-based estimator.Comment: 15 pages, 16 figure
An Empirical Bayes Approach for Multiple Tissue eQTL Analysis
Expression quantitative trait loci (eQTL) analyses, which identify genetic
markers associated with the expression of a gene, are an important tool in the
understanding of diseases in human and other populations. While most eQTL
studies to date consider the connection between genetic variation and
expression in a single tissue, complex, multi-tissue data sets are now being
generated by the GTEx initiative. These data sets have the potential to improve
the findings of single tissue analyses by borrowing strength across tissues,
and the potential to elucidate the genotypic basis of differences between
tissues.
In this paper we introduce and study a multivariate hierarchical Bayesian
model (MT-eQTL) for multi-tissue eQTL analysis. MT-eQTL directly models the
vector of correlations between expression and genotype across tissues. It
explicitly captures patterns of variation in the presence or absence of eQTLs,
as well as the heterogeneity of effect sizes across tissues. Moreover, the
model is applicable to complex designs in which the set of donors can (i) vary
from tissue to tissue, and (ii) exhibit incomplete overlap between tissues. The
MT-eQTL model is marginally consistent, in the sense that the model for a
subset of tissues can be obtained from the full model via marginalization.
Fitting of the MT-eQTL model is carried out via empirical Bayes, using an
approximate EM algorithm. Inferences concerning eQTL detection and the
configuration of eQTLs across tissues are derived from adaptive thresholding of
local false discovery rates, and maximum a-posteriori estimation, respectively.
We investigate the MT-eQTL model through a simulation study, and rigorously
establish the FDR control of the local FDR testing procedure under mild
assumptions appropriate for dependent data.Comment: accepted by Biostatistic
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