Smooth Sigmoid Surrogate (SSS): An Alternative to Greedy Search in Recursive Partitioning

Greedy search or exhaustive search plays a critical role in recursive partitioning and their extensions. We examine an alternative method by replacing the indicator threshold function involved in recursive partitioning with a smooth sigmoid surrogate (SSS) function. In many scenarios, it is important to formulate the problem appropriately, which can change the discrete greedy search for the best cutoff point into a one-dimensional continuous optimization problem. The proposed method can dramatically reduce the computational costs with greedy search. More importantly, it helps address the variable selection bias problem by borrowing statistical inference results available with parametric nonlinear regression models. Both simulations and real-data examples are provided to evaluate and illustrate its usage.