Learning a Tree-Structured Ising Model in Order to Make Predictions

Understand

We study the problem of learning a tree Ising model from samples such that subsequent predictions made using the model are accurate.

• The prediction task considered in this paper is that of predicting the values of a subset of variables given values of some other subset of variables.
• Virtually all previous work on graphical model learning has focused on recovering the true underlying graph.
• We define a distance ("small set TV" or ssTV) between distributions $P$ and $Q$ by taking the maximum, over all subsets $\mathcal{S}$ of a given size, of the total variation between the marginals of $P$ and $Q$ on $\mathcal{S}$; this distance captures the accuracy of the prediction task of interest.