Paper:
LightGBM: A Highly Efficient Gradient Boosting Decision Tree
Gradient Boosting Decision Tree (GBDT) is a popular machine learning algorithm, and has quite a few effective implementations such as XGBoost and pGBRT. Although many engineering optimizations have been adopted in these implementations, the efficiency and scalability are still unsatisfactory when the feature dimension is high and data size is large. A major reason is that for each feature, they need to scan all the data instances to estimate the information gain of all possible split points, which is very time consuming. To tackle this problem, we propose two novel techniques: Gradient-based One-Side Sampling (GOSS) and Exclusive Feature Bundling (EFB). With GOSS, we exclude a significant proportion of data instances with small gradients, and only use the rest to estimate the information gain. We prove that, since the data instances with larger gradients play a more important role in the computation of information gain, GOSS can obtain quite accurate estimation of the information gain with a much smaller data size. With EFB, we bundle mutually exclusive features (i.e., they rarely take nonzero values simultaneously), to reduce the number of features. We prove that finding the optimal bundling of exclusive features is NP-hard, but a greedy algorithm can achieve quite good approximation ratio (and thus can effectively reduce the number of features without hurting the accuracy of split point determination by much). We call our new GBDT implementation with GOSS and EFB LightGBM. Our experiments on multiple public datasets show that, LightGBM speeds up the training process of conventional GBDT by up to over 20 times while achieving almost the same accuracy.

Review:
The paper presents two nice ways for improving the usual gradient boosting algorithm where weak classifiers are decision trees. It is a paper oriented towards efficient (less costful)  implementation of the usual algorithm in order to speed up the learning of decision trees by taking into account previous computations and sparse data.
The approaches are interesting and smart. A risk bound is given for one of the improvements (GOSS), which seems sound but still quite loose: according to the experiments, a tighter bound could be obtained, getting rid of the "max" sizes of considered sets. No garantee is given for the second improvement (EFB) although is seems to be quite efficient in practice. 
The paper comes with a bunch of interesting experiments, which give good insights and shows a nice study of the pros and vons of the improving approaches, both in accuracy and computational time, in various types of datasets. The experiments lacks of standard deviation indications, for the performances are often very closed from one mathod to another. A suggestion would be to observe the effect of noise in the data on the improvement methods (especially on GOSS, which relies mostly on a greedy selection based on the highest gradients). 
The paper is not easy to read, because the presentation, explanation, experimental study and analysis are spread all over the paper. It would be better to concentrate fully on one improvements, then on the other, and to finish by the study of them together.  Besides, it would be helpfulfor the reader if the main algorithms where written in simplest ways, not in pseudo codes and assumption on the specificities of data structures.