Paper:
Nowadays, deep neural networks (DNNs) have become the main instrument for machine learning tasks within a wide range of domains, including vision, NLP, and speech. Meanwhile, in an important case of heterogenous tabular data, the advantage of DNNs over shallow counterparts remains questionable. In particular, there is no sufficient evidence that deep learning machinery allows constructing methods that outperform gradient boosting decision trees (GBDT), which are often the top choice for tabular problems. In this paper, we introduce Neural Oblivious Decision Ensembles (NODE), a new deep learning architecture, designed to work with any tabular data. In a nutshell, the proposed NODE architecture generalizes ensembles of oblivious decision trees, but benefits from both end-to-end gradient-based optimization and the power of multi-layer hierarchical representation learning. With an extensive experimental comparison to the leading GBDT packages on a large number of tabular datasets, we demonstrate the advantage of the proposed NODE architecture, which outperforms the competitors on most of the tasks. We open-source the PyTorch implementation of NODE and believe that it will become a universal framework for machine learning on tabular data.

Review:
This paper introduces a new method to make ensembles of decision trees differentiable, and trainable with (stochastic) gradient descent. The proposed technique relies on the concept of "oblivious decision trees", which are a kind of decision trees that use the same classifier (i.e. a feature and threshold) for all the nodes that have the same depth. This means that for an oblivious decision tree of depth d, only d classifiers are learned. Said otherwise, an oblivious decision tree is a classifier that split the data using d splitting features, giving a decision table of size 2^d. To make oblivious decision trees differentiable, the authors propose to learn linear classifiers using all the features, but add a sparsity inducing operator on the weights of the classifiers (the entmax transformation). Similarly, the step function used to split the data is replaced by a continuous version (here a binary entmax transformation). Finally, the decision function is obtained by taking the outer product of all the scores of the classifiers: [c_1(x), 1-c_1(x)] o [c_2(x), 1-c_2(x)] ... This "choice" operator transforms the d dimensional vectors of the classifier scores to a 2^d dimensional vector. Another interpretation of the proposed "differentiable oblivious decision trees" is a two layer neural network, with sparsity on the weights of the first layer,
and an activation function combining the entmax transformation and the outer product operator. The authors then propose to combine multiple differentiable decision trees in one layer, giving the neural decision oblivious ensemble (NODE). Finally, several NODE layers can be combined in a dense net fashion, to obtain a deep decision tree model. The proposed method is evaluated on 6 datasets (half classification, half regression), and compared to existing decision tree methods such as XGBoost or CatBoost, as well as feed forward neural networks.
The paper is clearly written, ideas are well presented, and it is easy to follow the derivation of the method. As a minor comment, I would suggest to the authors to give more details on the EntMax method, as it is quite important for the method, but not really introduced in the paper. The proposed algorithm is sound, and a nice way to make decision trees differentiable. One concern that I have though, is that it seems that NODE are close to fully connected neural networks, with sparsity on the weights. Indeed, I think that there are two ingredients in the paper to derive the method: adding sparsity to the weights and the outer product operator (as described in the previous paragraph). In particular, the improvement over vanilla feed forward neural networks seem small in the experimental section. I thus believe that it would be interesting to study if both two differences with feed forward networks are important, or if only is enough to get better results.
To conclude, I believe that this is a well written paper, proposing a differentiable version of decision trees which is interesting. However, the proposed method relies on existing techniques, such as EntMax, and I wonder if the (relatively small) improvement compared to feed forward network comes from these. I believe that it would thus be interesting to compare the method with feed forward network with sparsity on the weights. For now, I am putting a weak reject decision, but I am willing to reconsider my rating based on the author response.
Questions to the authors:
(1) do you use the same data preprocessing for all methods (quantile transform)?
(2) would it make sense to evaluate the effects of each the entmax and the outer product operator separately in the context of fully connected networks?