Minimum Description Length Learning

MDL Learning is basically another interpretation for MAP Learning where we interpret the log terms

similar to how we did with Information Gain in Decision Tree Induction, as the number of bits to encode data given the hypothesis

and the additional bits to encode the hypothesis

So to get the best hypothesis $h_{\text{MDL}}$ we have to minimize the Entropy of the hypothesis Likelihood.

Intuition
If the hypothesis predicts the data exactly, then $P(d\mid h_i)=1$ which yields $\log_2(1)=0$ bits. So this is the preferred hypothesis.