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Random Intersection Trees

Finding interactions between variables in large and high-dimensional datasets is often a serious computational challenge. Most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The drawback is that potentially informative high-order interactions may be overlooked. Here, we propose at an alternative approach for classification problems with binary predictor variables, called Random Intersection Trees. It works by starting with a maximal interaction that includes all variables, and then gradually removing variables if they fail to appear in randomly chosen observations of a class of interest. We show that informative interactions are retained with high probability, and the computational complexity of our procedure is of order $p^κ$ for a value of $κ$ that can reach values as low as 1 for very sparse data; in many more general settings, it will still beat the exponent $s$ obtained when using a brute force search constrained to order $s$ interactions. In addition, by using some new ideas based on min-wise hash schemes, we are able to further reduce the computational cost. Interactions found by our algorithm can be used for predictive modelling in