Problem $5$

$1(1)$

$3$ points possible $($graded$,$ results hidden$)$

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 $i+1$ is greater than

or equal to the likelihood after iteration $i,$ for all $i.$

False

Depending on the initialization, the likelihood of the data the algorithm converges to may be different.

True

False

We are estimating a mixture model with $K$ components. During random initialization, $p_1$ was assigned to be zero. $p_1$ could become non$-$zero as the

algorithm iterates.

False