<div>Interaction screening for high-dimensional problems has recently drawn much attention. In the literature, a variety of interaction screening approaches have been proposed for regression and classification problems. This talk will present our recent work on scalable regularization methods to interaction selection under hierarchical constraints for high dimensional data. A new regularization method, called Regularization Algorithm under Marginality Principle (RAMP), is proposed to compute hierarchy-preserving regularization solution paths efficiently. In contrast to existing regularization methods, RAMP avoids storing the entire design matrix and sidesteps complex constraints and penalties and is therefore feasible to ultra-high dimensional analysis. The new methods are further extended to handling binary responses. Theory and numerical results are also presented. </div>