Maximum likelihood
This section introduces a simple algorithm to learn all the parameters of a graphical model as we saw until now. In the first section, we had our first experience of learning such a model and we concluded by saying that the parameters can be learned locally for each variable. It means that, for each variable x having parents pa(x) in the graph, for each combination of the parents pa(x) we compute frequencies for each value of x. If the dataset is complete enough, then this leads to the maximum likelihood estimation of the graphical models.
For each variable x in the graphical modeling, and for each combination c of the values of the parents of pa(x) of x:
- Extract all the data points corresponding to the values in c
- Compute a histogram Hc on the value of x
-
Assign
Is that it? Yes it is, it's all you have to do. The difficult part is the extraction of the data points, which is a problem you can solve in R using the ddply or aggregate functions.
But why is it so simple?...
