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SUMMARY:Advances in Bayesian Latent Factor Modelling: The Incredible Shrin
 king Model - Daniel Merl (Duke University)
DTSTART:20080229T140000Z
DTEND:20080229T150000Z
UID:TALK10244@talks.cam.ac.uk
CONTACT:8048
DESCRIPTION:Recent advances in the methodology and application of Bayesian
  latent factor models are discussed.  Sparse latent factor modelling\, in 
 which the now-standard latent factor modelling framework is coupled with s
 o-called sparsity\, or variable selection\, prior distributions on regress
 ion parameters\, has found significant application in the analysis of data
  falling under the ``large p\, small n'' heading.  This includes applicati
 ons in genomics and finance\, for which a primary goal is to characterize 
 variation in a very high-dimensional response in terms of a concise set of
  factors with sparse loadings. \nA useful consequence of sparsity in facto
 r loadings is the increased opportunity for ascribing specific scientific 
 interpretation to the latent factors.  For example\, analysis of gene expr
 ession microarrays in cancer studies has uncovered latent factors that hav
 e been demonstrated to be useful for predicting certain clinical outcomes.
  The loadings associated with such factors therefore represent signatures\
 , in response-space\, of those outcomes. \n\nTo the extent that signatures
  with meaningful interpretations are thought to represent underlying struc
 tural features of the system under study\, such as groups of genes whose p
 atterns of co-expression have causal relationships with known phenotypes\,
  in many cases prior belief about latent factor structure in new data shou
 ld be informed by posterior inferences drawn previously on similar data.  
 We extend the current class of sparse latent factor models to include info
 rmative variable selection priors on both latent factor loadings and laten
 t factors.  Through this approach\, previously inferred signatures are pro
 jected onto and refined by new data.  Examples from cancer genomics demons
 trate how this sort of targeted latent factor search improves the scientif
 ic interpretability of the model\, and allows a direct query of the contri
 bution of a known signature towards explaining variation in new data. \n\n
 More generally\, this methodology defines a flexible class of factor model
 s that through the model fitting process ``shrinks'' to the minimum number
  of covariates and latent factors supported by the data.  In order to achi
 eve total shrinkage\, we describe a new type of nonparametric variable sel
 ection prior for the variance components of the model. The prior incorpora
 tes a hierarchical Dirichlet process to induce clustering of variance para
 meters within sample groups\, while borrowing information across groups to
  estimate mixture components. When a control group is present\, the prior 
 for non-control group variances places additional probablility on a point 
 mass located at the control variance.  In this way\, variances are cluster
 ed both within and across sample groups\, yielding a parsimonious represen
 tation of the degree of heteroscedasticity in the data. Hence\, the incred
 ible shrinking model. \n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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