Nonparametric logistic regression based on sparse triangulation over a compact domain

다국어 초록 (Multilingual Abstract)

Based on the investigation of logistic regression models utilizing sparse triangulation within a compact domain in R², this study addresses the limited research extending the triogram model to logistic regression. A primary challenge arises from the potential instability induced by a large number of vertices, hindering the effective modeling of complex relationships. To mitigate this challenge, we propose introducing sparsity to boundary vertices of the triangulation based on the Ramer-Douglas-Peucker algorithm and employing the K-means algorithm for adaptive vertex initialization. A second order coordinate-wise descent algorithm is adopted to implement the proposed method. Validation of the proposed algorithm’s stability and performance assessment are conducted using synthetic and handwritten digit data (LeCun et al., 1989). Results demonstrate the advantages of our method over existing methodologies, particularly when dealing with non-rectangular data domains.