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CATEGORIES:ML@CL Seminar Series
SUMMARY:Reparameterizing Bayesian PCA using Householder tr
ansformations to break the rotational symmetry. -
Rajbir Nirwan\, Department of Computer Science\, G
oethe University\, Frankfurt\, Germany
DTSTART;TZID=Europe/London:20201204T131500
DTEND;TZID=Europe/London:20201204T140000
UID:TALK151843AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/151843
DESCRIPTION:*Paper:*\n\nThis talk will be based on "this":http
://proceedings.mlr.press/v97/nirwan19a/nirwan19a.p
df paper.\n\n\n*Abstract:*\n\nWe consider probabil
istic PCA and related factor models from a Bayesia
n perspective. These models are in general not ide
ntifiable as the likelihood has a rotational symme
try. This gives rise to complicated posterior dist
ributions with continuous subspaces of equal densi
ty and thus hinders efficiency of inference as wel
l as interpretation of obtained parameters. In par
ticular\, posterior averages over factor loadings
become meaningless and only model predictions are
unambiguous. Here\, we propose a parameterization
based on Householder transformations\, which remov
e the rotational symmetry of the posterior. Furthe
rmore\, by relying on results from random matrix t
heory\, we establish the parameter distribution wh
ich leaves the model unchanged compared to the ori
ginal rotationally symmetric formulation. In parti
cular\, we avoid the need to compute the Jacobian
determinant of the parameter transformation. This
allows us to efficiently implement probabilistic P
CA 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\, Househo
lder transform.\n\n*About the Speaker:*\n\nNA\n\n*
Website:* NA\n\nPart of ML@CL Seminar Series focus
ing on early career researchers in topics relevant
to machine learning and statistics.
LOCATION:https://dtudk.zoom.us/j/65731683392
CONTACT:Francisco Vargas
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