Use base2 log in entropy calculation

[dodgejoel]

The scipy entropy function called supports a base argument that can be used. Of course, the original paper's proof applies when entropy is calculated in base 2 not base e.

[hlin117]

I don't think this is necessary. The function should work just as well with log_e compared to log_2. Is there any advantage to using log_2 instead of log_e?

I avoided log_2 in the original code here because it was unnecessary, and made the code perhaps harder to read.

[dodgejoel]

I think the theoretical results on optimality of the discretization obtained with this method specifically depend on the entropy calculations ,which enter into the decision to accept or reject a given cut-point, being calculated with log_2. At some point the authors even specifically call this out as a requirement for the validity of their results: "Note that this theorem requires that the entropy Ent(S) be defined using logarithms to the base 2" on page 1026.

I don't see how using a different base in the logarithm impacts code readability in a substantial way. When you say that the function works "just as well with log_e compared to log_2" what exactly do you mean?

[dodgejoel]

Perhaps you are claiming that the cut points produced will always be the same? Is it formally true that it does not matter which base is used in this algorithm?

[dodgejoel]

any response here?