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==A duality formula for variational inference==
[[File:CAVI algorithm explain.jpg|600px|thumb|right|Pictorial illustration of coordinate ascent variational inference algorithm by the duality formula <ref name=Yoon2021
The following theorem is referred to as a duality formula for variational inference.<ref name=Yoon2021/> It explains some important properties of the variational distributions used in variational Bayes methods.
{{EquationRef|3|Theorem}} Consider two [[probability spaces]] <math>(\Theta,\mathcal{F},P)</math> and <math>(\Theta,\mathcal{F},Q)</math> with <math>Q \ll P</math>. Assume that there is a common dominating [[probability measure]] <math>\lambda</math> such that <math>P \ll \lambda</math> and <math>Q \ll \lambda</math>. Let <math>h</math> denote any real-valued [[random variable]] on <math>(\Theta,\mathcal{F},P)</math> that satisfies <math>h \in L_1(P)</math>. Then the following equality holds
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