BOLT-SSI: A Statistical Approach to Screening Interaction Effects for Ultra-High Dimensional Data

Detecting interaction effects is a crucial step in various applications. In this paper, we first propose a simple method for sure screening interactions (SSI). SSI works well for problems of moderate dimensionality, without heredity assumptions. For ultra-high dimensional problems, we propose a fast algorithm, named "BOLT-SSI". This is motivated by that the interaction effects on a response variable can be exactly evaluated using the contingency table when they are all discrete variables. The numbers in contingency table can be collected in an efficient manner by Boolean representation and operations. To generalize this idea, we propose a discritization step such that BOLT-SSI is applicable for interaction detection among continuous variables. Statistical theory has been established for SSI and BOLT-SSI, guaranteeing their sure screening property. Experimental results demonstrate that SSI and BOLT-SSI can often outperform their competitors in terms of computational efficiency and statistical accuracy, especially for the data with more than 300,000 predictors. Based on results, we believe there is a great need to rethink the relationship between statistical accuracy and computational efficiency. The computational performance of a statistical method can often be greatly improved by exploring advantages of the computational architecture, and the loss of statistical accuracy can be tolerated.