Transcription of Part IX The EM algorithm - Stanford University
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Part IX The EM algorithm - Stanford University
CS229 Lecture notesTengyu Ma and Andrew NgMay 13, 2019 Part IXThe EM algorithmIn the previous set of notes, we talked about the EM algorithmas applied tofitting a mixture of Gaussians. In this set of notes, we give a broader viewof the EM algorithm , and show how it can be applied to a large family ofestimation problems with latent variables. We begin our discussion with avery useful result calledJensen s inequality1 Jensen s inequalityLetfbe a function whose domain is the set of real numbers. Recall thatfis a convex function iff (x) 0 (for allx R). In the case offtakingvector-valued inputs, this is generalized to the conditionthat its hessianHis positive semi-definite (H 0). Iff (x)>0 for allx, then we sayfisstrictlyconvex (in the vector-valued case, the corresponding statement isthatHmust be positive definite, writtenH >0). Jensen s inequality canthen be stated as a convex function, and letXbe a random :E[f(X)] f(EX).
The EM algorithm In the previous set of notes, we talked about the EM algorithm as applied to fitting a mixture of Gaussians. In this set of notes, we give a broader view of the EM algorithm, and show how it can be applied to a large family of estimation problems with latent variables. We begin our discussion with a
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