36,637 research outputs found
The Infinite Hierarchical Factor Regression Model
We propose a nonparametric Bayesian factor regression model that accounts for
uncertainty in the number of factors, and the relationship between factors. To
accomplish this, we propose a sparse variant of the Indian Buffet Process and
couple this with a hierarchical model over factors, based on Kingman's
coalescent. We apply this model to two problems (factor analysis and factor
regression) in gene-expression data analysis
The supervised hierarchical Dirichlet process
We propose the supervised hierarchical Dirichlet process (sHDP), a
nonparametric generative model for the joint distribution of a group of
observations and a response variable directly associated with that whole group.
We compare the sHDP with another leading method for regression on grouped data,
the supervised latent Dirichlet allocation (sLDA) model. We evaluate our method
on two real-world classification problems and two real-world regression
problems. Bayesian nonparametric regression models based on the Dirichlet
process, such as the Dirichlet process-generalised linear models (DP-GLM) have
previously been explored; these models allow flexibility in modelling nonlinear
relationships. However, until now, Hierarchical Dirichlet Process (HDP)
mixtures have not seen significant use in supervised problems with grouped data
since a straightforward application of the HDP on the grouped data results in
learnt clusters that are not predictive of the responses. The sHDP solves this
problem by allowing for clusters to be learnt jointly from the group structure
and from the label assigned to each group.Comment: 14 page
Region-Referenced Spectral Power Dynamics of EEG Signals: A Hierarchical Modeling Approach
Functional brain imaging through electroencephalography (EEG) relies upon the
analysis and interpretation of high-dimensional, spatially organized time
series. We propose to represent time-localized frequency domain
characterizations of EEG data as region-referenced functional data. This
representation is coupled with a hierarchical modeling approach to multivariate
functional observations. Within this familiar setting, we discuss how several
prior models relate to structural assumptions about multivariate covariance
operators. An overarching modeling framework, based on infinite factorial
decompositions, is finally proposed to balance flexibility and efficiency in
estimation. The motivating application stems from a study of implicit auditory
learning, in which typically developing (TD) children, and children with autism
spectrum disorder (ASD) were exposed to a continuous speech stream. Using the
proposed model, we examine differential band power dynamics as brain function
is interrogated throughout the duration of a computer-controlled experiment.
Our work offers a novel look at previous findings in psychiatry, and provides
further insights into the understanding of ASD. Our approach to inference is
fully Bayesian and implemented in a highly optimized Rcpp package
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