Introduction to the EM algorithm - Department of Statistics

Introduction
Suppose we have data y 1 , . . . , y n that comes from a mixture of M
distributions, that is,
where
p(y i |θ) =
M∑
α j p j (y i |λ j )
j=1
λ j is the vector with the parameters of the jth distribution;
0 ≤ α j ≤ 1 for each j and ∑ M
j=1 α j = 1;
θ = (α 1 , . . . , α J , λ 1 , . . . , λ M ).
Camila Souza (UBC) Introduction to the EM algorithm November 2010 2 / 25