Deep Lattice Networks and Partial Monotonic Functions
We propose learning deep models that are monotonic with respect to a userspecified 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.
This paper proposes a novel deep model that is monotonic to user specified inputs, called deep lattice networks (DLN's), which is composed of layers of linear embeddings,  ensembles of
 lattices and calibrators. The results about the function classes of DLN's are also provided. 
Authors should put more effort to make the paper readable for the people that are not familiar with the technicality.  However the contributions are interesting and significant. As [3] proposed a 2 layer model,  which has a layer of calibrators followed by an ensemble of lattices, the advantages of proposed deeper model could be presented in a more convincing way by showing better results as the results seem closer to Crystals and it is not clear whether the produced results are stable. 
The computational complexity should be also discussed clearly.  Each projection step in optimization should be explained in more detail. What is the computational complexity of the projection for the calibrator? What proportion of training time the projections take?  Are the projections accurate or suboptimal in the first iterations? And how the overall training time compares to baselines?
Does the training of the proposed model produces bad local minima for deeper models? At most how many layers could be trained with current optimization procedure?
It seems most of the results are based on the data that is not publicly available. To make the results reproducible, authors should add more publicly available data to experiments. Also artificial data  would help to demonstrate some sanity checks, e.g. a case that two layer [3] did not work well but deeper model work better, the intermediate layer visualizations etc . 
Authors should also explain better why the model has interpretability and debuggability advantages.