Learning with continuous piecewise linear decision trees

In this paper, we propose a piecewise linear decision tree and its generalized form, namely the (G)PWL-DT, which introduces linearity overcomes discontinuity of existing constant trees (PWC-DT). The proposed (G)PWL-DT inherits basic topology interpretability by recursively partitioning domain into subregions, are represented leaf nodes. Rather than indicator function, employs rectifier units (ReLU) to interpret partitions, where nested ReLUs combined formulate corresponding PWL rules. Due each node, additional boundaries among areas obtained approach greater flexibility PWC-DT under same structure, continuity can also be guaranteed. Then, an optimization algorithm is constructed analogously based on second-order approximation. flexibly applied as novel in different learning methods it regarded simple extension framework learning. Numerical experiments verify effectiveness potential alternative better performance even with more concise structures.