Variational Bayesian methods: Difference between revisions

Revision as of 00:10, 21 April 2022

Revision as of 11:50, 29 April 2022

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: <math>P(\mathbf{Z}\mid \mathbf{X}) \approx Q(\mathbf{Z}).</math>

The distribution <math>Q(\mathbf{Z})</math> is restricted to belong to a family of distributions of simpler form (e.g. a family of Gaussian distributions) than <math>P(\mathbf{Z}\mid \mathbf{X})</math> (e.g. a family of Gaussian distributions), selected with the intention of making <math>Q(\mathbf{Z})</math> similar to the true posterior, <math>P(\mathbf{Z}\mid \mathbf{X})</math>.

The similarity (or dissimilarity) is measured in terms of a dissimilarity function <math>d(Q; P)</math> and hence inference is performed by selecting the distribution <math>Q(\mathbf{Z})</math> that minimizes <math>d(Q; P)</math>.