Deep Lattice Networks and Partial Monotonic Functions

TL;DR

This paper introduces deep lattice networks that enforce monotonicity constraints with respect to specific inputs, combining layers of linear embeddings, lattice ensembles, and calibrators, trained jointly for improved predictive performance.

Contribution

It presents a novel architecture for deep models that guarantees monotonicity, using a combination of lattice layers and new computational graph implementations in TensorFlow.

Findings

Achieves state-of-the-art performance on benchmark datasets.

Provides monotonicity guarantees in deep models.

Demonstrates effectiveness on real-world classification and regression tasks.

Abstract

We propose learning deep models that are monotonic with respect to a user-specified set of inputs by alternating layers of linear embeddings, ensembles of lattices, and calibrators (piecewise linear functions), with appropriate constraints for monotonicity, and jointly training the resulting network. We implement the layers and projections with new computational graph nodes in TensorFlow and use the ADAM optimizer and batched stochastic gradients. Experiments on benchmark and real-world datasets show that six-layer monotonic deep lattice networks achieve state-of-the art performance for classification and regression with monotonicity guarantees.