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SUMMARY:Reparameterizing Bayesian PCA using Householder transformations to
  break the rotational symmetry. - Rajbir Nirwan\, Department of Computer S
 cience\, Goethe University\, Frankfurt\, Germany
DTSTART:20201204T131500Z
DTEND:20201204T140000Z
UID:TALK151843@talks.cam.ac.uk
CONTACT:Francisco Vargas
DESCRIPTION:*Paper:*\n\nThis talk will be based on "this":http://proceedin
 gs.mlr.press/v97/nirwan19a/nirwan19a.pdf paper.\n\n\n*Abstract:*\n\nWe con
 sider probabilistic PCA and related factor models from a Bayesian perspect
 ive. These models are in general not identifiable as the likelihood has a 
 rotational symmetry. This gives rise to complicated posterior distribution
 s with continuous subspaces of equal density and thus hinders efficiency o
 f inference as well as interpretation of obtained parameters. In particula
 r\, posterior averages over factor loadings become meaningless and only mo
 del predictions are unambiguous. Here\, we propose a parameterization base
 d on Householder transformations\, which remove the rotational symmetry of
  the posterior. Furthermore\, by relying on results from random matrix the
 ory\, we establish the parameter distribution which leaves the model uncha
 nged compared to the original rotationally symmetric formulation. In parti
 cular\, we avoid the need to compute the Jacobian determinant of the param
 eter transformation. This allows us to efficiently implement probabilistic
  PCA in a rotation invariant fashion in any state of the art toolbox. Here
 \, we implemented our model in the probabilistic programming language Stan
  and illustrate it on several examples. \n\n*Keywords:* Probabilistic PCA\
 , Bayesian pPCA\, Disentangled Representations\, Rotational Invariance\, H
 ouseholder transform.\n\n*About the Speaker:*\n\nNA\n\n*Website:* NA\n\nPa
 rt of ML@CL Seminar Series focusing on early career researchers in topics 
 relevant to machine learning and statistics.
LOCATION:https://dtudk.zoom.us/j/65731683392
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