Algorithm 3. Expectation maximization algorithm for BN learning

Step 0: Initiate μ to μ0 and set μt = μ0 and then continue; Step 1: To compute μt+1 once μt is known, complete Step 2 and Step 3; Step 2: Expectation step: compute the data set based on μt: a) Compute the conditional probability distribution of missing values v* using the Bayesian formula as follows:   $P(v*|v,{\mu }^t)=\frac{P(v*,{\mu }^t)P(v|v*,{\mu }^t)}{{\displaystyle {\sum }_{v*}P(v*,{\mu }^t)P(v|v*,{\mu }^t)}}$, where v is the set of observed values. b) Obtain the fractional value by assigning a weight, given as $P(v*|v,{\mu }^t)$, to the missing values v*, and add the value into the incomplete data set to construct the completed data set. Step 3: Maximization Step: To obtain the MLE of the model parameters μt+1, compute the set of parameters that maximize the likelihood of the completed data set acquired in Step 2b. Step 4: If convergence is obtained, the algorithm stops; if not, make t = t+1 and μt = μt+1, and return to Step 1.