The index m in finite mixture models, as in Eq. (12.1), can be extended to be a continuous variable y 2 R:

This is called an infinite mixture model if ¯
w¹yº dy = 1 and ¯
p¹x j , yº dx = 1 (8, y) hold. Extend the EM algorithm to the infinite mixture models:

a. Define the auxiliary function for an infinite mixture model.

b. Design the E-step and M-step for an infinite mixture model.

Transcribed Image Text:

p(x) = ) = w(y)p(x|0, y) dy.