M-Step of the EM Algorithm
Holding responsibilities fixed, maximize Q in closed form: each mu_k becomes the responsibility-weighted mean, Sigma_k the weighted covariance, and pi_k = N_k / N where N_k is the effective count; the sum-to-one constraint on pi is handled with a Lagrange multiplier.
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Holding responsibilities fixed, maximize Q in closed form: each mu_k becomes the responsibility-weighted mean, Sigma_k the weighted covariance, and pi_k = N_k / N where N_k is the effective count; the sum-to-one constraint on pi is handled with a Lagrange multiplier.
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