Factor models
for QTL studies
Oliver Stegle at the 2008 Workshop on Learning and Inference in
Computational Systems Biology, Glasgow
The recent availability of large scale data sets profiling single
nucleotide polymorphisms (SNPs) and gene expression across different
human populations, has directed much attention towards discovering
patterns of genetic variation and their association with gene
regulation. Two aspects of the nature of expression profiles make the
identification and interpretation of such associations
difficult. Firstly, we expect that a variety of environmental,
developmental and other factors influence gene expression which can
obscure such associations. Secondly, the regulatory network linking genes
makes it difficult to pinpoint causal relationships between SNPS and
regulatory elements. We address the first issue by proposing FA-eQTL, a
factor-model that explicitly takes non-genetic variability into account,
and thereby can significantly improve the power of an expression
Quantitative Trait Loci (eQTL) study. We discuss a variational Bayesian
implementation of this model, and point out rapid approximations that are
applicable in certain situations. Applying our model to simulated and
real world data we can demonstrate a significant improvement in
performance. On data from the HapMap project, we find more than three
times as many significant associations than a standard eQTL method. To
address co-expression of genes, we further extended FA-eQTL by jointly
reducing the dimensionality of the ex-pression profile and modelling
non-genetic factors. We discuss results applying this enhanced QTL-model
to biological data, including human as well as datasets from yeast.
|
|
Nonparametric
Bayesian Density Modeling with Gaussian Processes
Ryan Adams at the 2008 ICML/UAI/COLT Workshop on Nonparametric Bayes, Helsinki
We present the Gaussian Process Density Sampler (GPDS), an exchangeable
generative model for use in nonparametric Bayesian density
estimation. Samples drawn from the GPDS are consistent with exact,
independent samples from a fixed density function that is a
transformation of a function drawn from a Gaussian process prior. Our
formulation allows us to infer an unknown density from data using Markov
chain Monte Carlo, which gives samples from the posterior distribution
over density functions and from the predictive distribution on data
space. We describe two such MCMC methods. Both methods also allow
inference of the hyperparameters of the Gaussian process.
|
|
Gaussian
Process Product Models for Nonparametric Nonstationarity
Oliver Stegle at the 2008 International Conference on Machine
Learning, Helsinki
Stationarity is often an unrealistic prior assumption for Gaussian process
regression. One solution is to predefine an explicit nonstationary
covariance function, but such covariance functions can be difficult to
specify and require detailed prior knowledge of the nonstationarity. We
propose the Gaussian process product model (GPPM) which models data as the
pointwise product of two latent Gaussian processes to nonparametrically
infer nonstationary variations of amplitude. This approach differs from
other nonparametric approaches to covariance function inference in that it
operates on the outputs rather than the inputs, resulting in a significant
reduction in computational cost and required data for inference, while
improving scalability to high-dimensional input spaces. We present an
approximate inference scheme using Expectation Propagation. This
variational approximation yields convenient GP hyperparameter selection and
compact approximate predictive distributions.
|
|
