# Hierarchical Lattice Layer for Partially Monotone Neural Networks

## Abstract

Partially monotone regression is a regression analysis in which the target values are monotonically increasing with respect to a subset of input features. The TensorFlow Lattice library is one of the standard machine learning libraries for partially monotone regression. It consists of several neural network layers, and its core component is the lattice layer. One of the problems of the lattice layer is its requirement for a special training algorithm to satisfy monotonicity constraints. Another problem is that it cannot receive a high-dimensional input vector due to the resultant memory consumption. We propose a novel neural network layer, the hierarchical lattice layer (HLL), as an extension of the lattice layer so that we can use a standard neural network algorithm to train HLL while satisfying monotonicity constraints and so that it can receive a high-dimensional input vector. Our experiments demonstrate that HLL did not sacrifice its prediction performance on real datasets compared with the lattice layer.