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SUMMARY:Rotation Invariant Householder Parameterization for Bayesian PCA -
  Rajbir Nirwan\, Goethe University\, Frankfurt
DTSTART:20190904T100000Z
DTEND:20190904T110000Z
UID:TALK128551@talks.cam.ac.uk
CONTACT:Robert Peharz
DESCRIPTION:We consider probabilistic PCA and related factor models from a
  Bayesian perspective. These models are in general not identifiable as the
  likelihood has a rotational symmetry. This gives rise to complicated post
 erior distributions with continuous subspaces of equal density and thus hi
 nders efficiency of inference as well as interpretation of obtained parame
 ters. In particular\, posterior averages over factor loadings become meani
 ngless and only model predictions are unambiguous. In our paper\, we propo
 se a parameterization based on Householder transformations\, which remove 
 the rotational symmetry of the posterior. Furthermore\, by relying on resu
 lts from random matrix theory\, we establish the parameter distribution wh
 ich leaves the model unchanged compared to the original rotationally symme
 tric formulation. In particular\, we avoid the need to compute the Jacobia
 n determinant of the parameter transformation. This allows us to efficient
 ly implement probabilistic PCA in a rotation invariant fashion in any stat
 e of the art toolbox. We implemented our model in the probabilistic progra
 mming language Stan and illustrate it on several examples.
LOCATION:Engineering Department\, CBL Room BE-438.
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