Wan Zhang Research Project

Wan Zhang (UNC STOR grad)

Title: Regularization of BELIEF under Smoothness Interpretations

Abstract: As the complexity of models and the volumes 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 obstable, we propose a novel definition of smoothness for binary interactions and create a regularization of BELIEF under smoothness interpretations. We prove that there is a one-one correspondence between each marginal binary interaction and the smoothness we defined. Additionally, we have shown that in higher dimensions, the smoothness can be expressed as a product of that for marginal binary interactions. Based on these observations, we propose to model the smooth form of dependency with a generalized LASSO model with larger penalty on less smooth terms. The numerical studies show that the smooth LASSO takes advantages in clear interpretability and effectiveness for nonlinear and highh dimensional data.