10 research outputs found
The correlation space of Gaussian latent tree models and model selection without fitting
We provide a complete description of possible covariance matrices consistent
with a Gaussian latent tree model for any tree. We then present techniques for
utilising these constraints to assess whether observed data is compatible with
that Gaussian latent tree model. Our method does not require us first to fit
such a tree. We demonstrate the usefulness of the inverse-Wishart distribution
for performing preliminary assessments of tree-compatibility using
semialgebraic constraints. Using results from Drton et al. (2008) we then
provide the appropriate moments required for test statistics for assessing
adherence to these equality constraints. These are shown to be effective even
for small sample sizes and can be easily adjusted to test either the entire
model or only certain macrostructures hypothesized within the tree. We
illustrate our exploratory tetrad analysis using a linguistic application and
our confirmatory tetrad analysis using a biological application.Comment: 15 page
A hierarchical Bayesian network approach for linkage disequilibrium modeling and data-dimensionality reduction prior to genome-wide association studies
<p>Abstract</p> <p>Background</p> <p>Discovering the genetic basis of common genetic diseases in the human genome represents a public health issue. However, the dimensionality of the genetic data (up to 1 million genetic markers) and its complexity make the statistical analysis a challenging task.</p> <p>Results</p> <p>We present an accurate modeling of dependences between genetic markers, based on a forest of hierarchical latent class models which is a particular class of probabilistic graphical models. This model offers an adapted framework to deal with the fuzzy nature of linkage disequilibrium blocks. In addition, the data dimensionality can be reduced through the latent variables of the model which synthesize the information borne by genetic markers. In order to tackle the learning of both forest structure and probability distributions, a generic algorithm has been proposed. A first implementation of our algorithm has been shown to be tractable on benchmarks describing 10<sup>5 </sup>variables for 2000 individuals.</p> <p>Conclusions</p> <p>The forest of hierarchical latent class models offers several advantages for genome-wide association studies: accurate modeling of linkage disequilibrium, flexible data dimensionality reduction and biological meaning borne by latent variables.</p
Finding the Right Tree: Topology Inference Despite Spatial Dependences
© 1963-2012 IEEE. Network tomographic techniques have almost exclusively been built on a strong assumption of mutual independence of link processes. We introduce model classes for link loss processes with non-Trivial spatial dependencies, for which the tree topology is nonetheless identifiable from leaf measurements using multicast probing. We show that these classes are large in a well-defined sense, and we provide an algorithm, SLTD, capable of returning the correct topology with certainty in the limit of infinite data