Description

As the complexity of models and the volume of data increase, interpretable methods for modeling complicated dependence are in great need. A recent framework of binary expansion linear effect (BELIEF) provides a ``divide and conquer'' approach to decompose any complex form of dependency into small linear regressions over data bits. Although BELIEF can be used to approximate any relationship, it faces an important challenge of high dimensionality. To overcome this obstacle, we propose a novel definition of smoothness for binary interactions {through an interesting connection to the sequency of Walsh functions. We investigate this connection and study related theory and algorithms. Based on the connection}, we create a regularization of BELIEF under smoothness interpretations. In particular, we propose to model smooth forms of dependency with a generalized lasso model, which we call the sequency lasso, with larger penalty on less smooth terms. The numerical studies demonstrate that the proposed sequency lasso has advantages in clear interpretability and effectiveness for nonlinear and high dimensional data.