In this popular question, high upvoted answer makes MLE and Baum Welch separate in HMM fitting.
For training problem we can use the following 3 algorithms: MLE (maximum likelihood estimation), Viterbi training(DO NOT confuse with Viterbi decoding), Baum Welch = forward-backward algorithm
BUT in Wikipedia, it says
The Baum–Welch algorithm uses the well known EM algorithm to find the maximum likelihood estimate of the parameters
So, what's the relationship between MLE and Baum–Welch algorithm?
My attempt: The objective for Baum–Welch algorithm is maximize likelihood, but it uses a specialized algorithm (EM) to solve the optimization. We still can maximize likelihood by using other methods such as gradient decent. This is why the answer make two algorithm separate.
Am I right and can anyone help me to clarify?