CS 2750: Machine Learning Expectation Maximization

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Presentation transcript:

CS 2750: Machine Learning Expectation Maximization Prof. Adriana Kovashka University of Pittsburgh March 28, 2016

Mixtures of Gaussians Form: Let z (latent variable) be 1-of-K representation, then Responsibility of component k for explaining x:

Generating samples Sample value z* from p(z) then sample a value for x from p(x|z*) Color generated samples using z* (left) Color samples using responsibilities (right)

Finding parameters of mixture Want to maximize: Set derivative with respect to means to 0, get

Finding parameters of mixture Set derivative wrt covariance to 0: Set derivative wrt mixing coefficients to 0:

Reminder Responsibilities: So parameters of Gaussian depend on responsibilities and vice versa… Remember K-means?

Iterative algorithm From Bishop

From Bishop

General algorithm From Bishop