Populating Transition Matrix: Smoothing

The denominator shows “*NX(N+1)epsilon” and not “NXepsilon”. See the illustration below.

You show a four-by-three matrix, thus 12 entries; there is an epsilon for each entry I,j. There should be 12 epsilons for the matrix, which you show on the far right row sum column for each row.
However, the denominator in your smoothing equation show N (which would be 3). The right column shows n* (n+1) = 3 * (3+1)= 3X4 = 12 epsilons.

Are you normalizing each row separately? Please elaborate.


Yes. For example, first row tells you P(NN|\pi), P(VB|\pi), P(O|\pi). If you smooth the probabilities by adding \epsilon, you have to have that many \epsilon added to the denominator (3 in this case), that way you get the probabilities for this row to sum to 1.


Thanks, got it after a bit more reading.