# Implement Baum-Welch Learning solved by 32

Sept. 16, 2015, 3 a.m. by Rosalind Team

Topics: HMM

## Baum-Welch Learning Problem

Given: A sequence of emitted symbols x = x1 . . . xn in an alphabet A, generated by a k-state HMM with unknown transition and emission probabilities, initial Transition and Emission matrices and a number of iterations I.

Return: A matrix of transition probabilities Transition and a matrix of emission probabilities Emission that maximizes Pr(x,π) over all possible transition and emission matrices and over all hidden paths π.

## Sample Dataset

10
--------
xzyyzyzyxy
--------
x   y   z
--------
A   B
--------
A   B
A   0.019   0.981
B   0.668   0.332
--------
x   y   z
A   0.175   0.003   0.821
B   0.196   0.512   0.293


## Sample Output

A   B
A   0.000   1.000
B   0.786   0.214
--------
x   y   z
A   0.242   0.000   0.758
B   0.172   0.828   0.000