The minimum description length, aka, MDL, is based on the relations between regularity and data compression. (See for more about data descriptions.).

In statistical inferences, given a dataset $\mathcal D$, the compressions of the data is our model $\mathcal M$, or hypothesis $\mathcal H$ in the language of hypothesis testing.

MDL looks for the model that compresses the data well but with a reasonable cost of complexity. The complexity of the model is described by a length $L(\mathcal M)$, the goodness of the model is $G$. MDL looks into the balance of $L(\mathcal M)$ and $G$. For example, one could calculate the length of the model using the number of parameters $k$ in the model, and the goodness of the model using likelihood $p(\mathcal D \mid \mathcal M)$.

There are many versions of MDL: 1

• crude two-part code,
• Fisher information approximation ( ),
• Normalized Maximum likelihood ( ).

Planted: by ;

L Ma (2020). 'Minimum Description Length', Datumorphism, 11 April. Available at: https://datumorphism.leima.is/cards/statistics/mdl/.