Question

Mark the following statements as true or false. The EM algorithm monotonically increases the likelihood of the data with each iteration. In other words, the likelihood after iteration is greater than or equal to the likelihood after iteration , for all .

Answer 1

True. The Expectation-Maximization (EM) algorithm is designed to iteratively improve the likelihood of the data. Specifically, in each iteration, the E-step (Expectation step) computes the expected value of the log-likelihood given the current parameters, and the M-step (Maximization step) optimizes these parameters to maximize the expected log-likelihood. As a result, the likelihood of the observed data is guaranteed to not decrease with each iteration, meaning that the likelihood after iteration \( t \) is always greater than or equal to the likelihood after iteration \( t-1 \) for all \( t \).