Mixture models on graphs
published: Sept. 7, 2007, recorded: September 2007, views: 4147
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One of the most fundamental challenges in the analysis of 'omics data sets is clustering the relevant quantities (gene transcripts, protein levels, etc.) into distinct groups. One of the simplest instances occurs when comparing data obtained from two different conditions, where the basic task is to assess whether a quantity is upregulated, downregulated or unregulated. This task has traditionally been addressed using t-statistics or, from a probabilistic point of view, mixture models, with one mixture representing one of the three states of regulation. This approach tacitly assumes the various measurements to be independently drawn from the same mixture distribution. However, it is well known that biological quantities (genes, enzymes, etc.) are not independent, but they are linked in an often very complex network of interactions at various levels. It is therefore reasonable to use available network structure (and weighting) information in order to obtain a more accurate inference of the expression state. This can also be found useful in finding suitable subnetworks that exhibit coherent behaviours, giving rise to testable biological predictions. In this contribution, we introduce a probabilistic model that implements mixture models on a graph. The graph structure is encoded in a set of conditional prior distributions over the latent class memberships. This formulation leads naturally to a Gibbs sampling approach. We present preliminary results on synthetic and real data where gene expression is modelled as a mixture of a Gaussian and two exponential distributions.
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