Select the formula(s) for E-steps and M-steps. (Choose all that apply).
E-step: update Qti(z(i)) based on x(i) and the previous value of θt−1 .
Qti(z(i)):=P(z(i),x(i)|θt−1)
Qti(z(i)):=P(z(i)|x(i),θt−1)
Qti(z(i)):=P(x(i)|z(i),θt−1)
M-step: update θt based on the current value of Qti(z(i)) .
θt:=argmaxθ∑mi=1∑z(i)∈ZQti(z(i))logP(x(i),z(i)|θ)
θt:=argmaxθ∑mi=1∑z(i)∈ZP(z(i)|x(i),θt−1)logP(x(i),z(i)|θ)
θt:=argmaxθ∑mi=1∑z(i)∈ZP(z(i)|x(i),θ)logP(x(i),z(i)|θ)
θt:=argmaxθ∑mi=1∑z(i)∈ZP(x(i)|z(i),θt−1)logP(x(i),z(i)|θ)
E-step: The formula for the E-step is:
Qti(z(i)):=P(z(i),x(i)|θt−1)
This formula calculates the probability of observing a latent variable z(i) and data point x(i) given the previous value of the parameter θt−1.
M-step: The formula for the M-step is:
θt:=argmaxθ∑mi=1∑z(i)∈ZQti(z(i))logP(x(i),z(i)|θ)
This formula updates the value of the parameter θt based on the current values of Qti(z(i)). It maximizes the log-likelihood of the observed data x(i) and latent variables z(i) under the parameter θ.