Threshold Boundary Logistic Regression for Binary Data

Abstract

This talk introduces Threshold Boundary Logistic Regression (TBLR) for binary outcomes, which links covariates to both the logistic component and a linear or nonlinear threshold that partitions the feature space for distinct logistic models. We develop an iterative two-stage sample-splitting estimator that recasts the non-differentiable likelihood into an optimization: threshold parameters are obtained by minimizing a weighted classification loss, while logistic parameters are updated by likelihood maximization. Under suitable conditions, we establish consistency, oracle-optimal convergence rates, and asymptotic normality. Computation uses both Mixed-Integer Programming (MIP) and Weighted SVM (WSVM) as solvers: for linear boundaries we warm-start MIP with a WSVM solution—improving estimation at extra runtime—whereas nonlinear boundaries are solved by WSVM only. Simulations and real-data analyses illustrate finite-sample behavior and feasibility in nonlinear regimes. We further outline an extension to count responses—Threshold Boundary Poisson Regression (TBPR)—adapting the two-stage scheme to the Poisson likelihood and log link, and we will present preliminary empirical analyses that demonstrate applicability and the modeling workflow for count data.

Keywords：Maximum likelihood (ML), mixed integer programming (MIP), two-stage sample-splitting, weighted support vector machine (WSVM).

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