Transcription of Variational Inference - Princeton University
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Variational Inference - Princeton University
Variational InferenceDavid M. Blei1 Set up As usual, we will assume thatx=x1:nare observations andz=z1:mare hiddenvariables. We assume additional parameters that are fixed. Note we are general the hidden variables might include the parameters, , in atraditional Inference setting. (In that case, are the hyperparameters.) We are interested in theposterior distribution,p(z|x, ) =p(z,x| ) zp(z,x| ).(1) As we saw earlier, the posterior links the data and a model. It is used in all downstreamanalyses, such as for the predictive distribution. (Note: The problem of computing the posterior is an instance of a more general problemthat Variational Inference solves.)2 Motivation We can t compute the posterior for many interesting models.
inference is one of the central problems in Bayesian statistics. 3 Main idea We return to the general fx;zgnotation. The main idea behind variational methods is to pick a family of distributions over the latent variables with its own variational parameters, q(z 1:mj ): (5) Then, nd the setting of the parameters that makes qclose to the ...
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