Expectation-Maximization Algorithm Quiz

Answers and explanations appear as you take the quiz.

1. What does the E-step calculate using current parameters?
   • Conditional expectations of complete-data quantities or log likelihood
   • The global maximum of observed likelihood
   • Hard labels for every hidden variable by necessity
   • A new validation dataset
2. In a Gaussian mixture, what do responsibilities represent?
   • Fixed labels known before fitting
   • Posterior membership probabilities for observations across components
   • Component means multiplied by covariances
   • The number of EM iterations remaining
3. What does the M-step do after expectations are computed?
   • Changes the number of features automatically
   • Replaces all observations with component labels
   • Maximizes the expected complete-data objective over parameters
   • Computes the validation likelihood only
4. What guarantee does exact EM provide under suitable assumptions?
   • The selected model is scientifically correct
   • It finds the unique global optimum
   • Every hidden assignment becomes certain
   • Observed-data likelihood does not decrease at each iteration
5. Different EM initializations end at different likelihoods. What does this suggest?
   • The E-step is unnecessary
   • The optimization is sensitive to starts and may have local optima
   • The data contain no latent variables
   • All parameter estimates are unbiased
6. Why are mixture responsibilities not automatically hard assignments?
   • They are class labels copied from the target
   • They are always equal for every observation
   • They are probabilities that can distribute one observation across components
   • They represent only missing data
7. What does a small likelihood improvement at stopping indicate?
   • The latent structure has causal meaning
   • The model is proven adequate
   • The global optimum is certain
   • The chosen numerical convergence criterion was met
8. How does generalized EM differ from exact EM?
   • Its M-step may increase the expected objective without fully maximizing it
   • It removes the latent variables
   • It guarantees a global optimum
   • It replaces likelihood with classification accuracy