Predictive Discretization during Model Selection


Harald Steck, Tommi S. Jaakkola ;
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:532-539, 2007.


We present an approach to discretizing multivariate continuous data while learning the structure of a graphical model. We derive the joint scoring function from the principle of predictive accuracy, which inherently ensures the optimal trade-off between goodness of fit and model complexity (including the number of discretization levels). Using the so-called finest grid implied by the data, our scoring function depends only on the number of data points in the various discretization levels. Not only can it be computed efficiently, but it is also invariant under monotonic transformations of the continuous space. Our experiments show that the discretization method can substantially impact the resulting graph structure.

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