This is a conceptual overview of how LightGBM works\ `[1] <#references>`__. We assume familiarity with decision tree boosting algorithms to focus instead on aspects of LightGBM that may differ from other boosting packages. For detailed algorithms, please refer to the citations or source code.
Many boosting tools use pre-sort-based algorithms\ `[2, 3] <#references>`__ (e.g. default algorithm in xgboost) for decision tree learning. It is a simple solution, but not easy to optimize.
LightGBM uses histogram-based algorithms\ `[4, 5, 6] <#references>`__, which bucket continuous feature (attribute) values into discrete bins. This speeds up training and reduces memory usage. Advantages of histogram-based algorithms include the following:
- Computing the histogram has time complexity ``O(#data)``, but this involves only a fast sum-up operation. Once the histogram is constructed, a histogram-based algorithm has time complexity ``O(#bins)``, and ``#bins`` is far smaller than ``#data``.
- So it needs to construct histograms for only one leaf (with smaller ``#data`` than its neighbor). It then can get histograms of its neighbor by histogram subtraction with small cost (``O(#bins)``)
:alt:A diagram depicting level wise tree growth in which the best possible node is split one level down. The strategy results in a symmetric tree, where every node in a level has child nodes resulting in an additional layer of depth.
Leaf-wise may cause over-fitting when ``#data`` is small, so LightGBM includes the ``max_depth`` parameter to limit tree depth. However, trees still grow leaf-wise even when ``max_depth`` is specified.
:alt:A diagram depicting leaf wise tree growth in which only the node with the highest loss change is split and not bother with the rest of the nodes in the same level. This results in an asymmetrical tree where subsequent splitting is happening only on one side of the tree.
It is common to represent categorical features with one-hot encoding, but this approach is suboptimal for tree learners. Particularly for high-cardinality categorical features, a tree built on one-hot features tends to be unbalanced and needs to grow very deep to achieve good accuracy.
Instead of one-hot encoding, the optimal solution is to split on a categorical feature by partitioning its categories into 2 subsets. If the feature has ``k`` categories, there are ``2^(k-1) - 1`` possible partitions.
But there is an efficient solution for regression trees\ `[8] <#references>`__. It needs about ``O(k * log(k))`` to find the optimal partition.
The basic idea is to sort the categories according to the training objective at each split.
More specifically, LightGBM sorts the histogram (for a categorical feature) according to its accumulated values (``sum_gradient / sum_hessian``) and then finds the best split on the sorted histogram.
It only needs to use some collective communication algorithms, like "All reduce", "All gather" and "Reduce scatter", in distributed learning of LightGBM.
Since feature parallel cannot speed up well when ``#data`` is large, we make a little change: instead of partitioning data vertically, every worker holds the full data.
Thus, LightGBM doesn't need to communicate for split result of data since every worker knows how to split data.
And ``#data`` won't be larger, so it is reasonable to hold the full data in every machine.
If using collective communication algorithm (e.g. "All Reduce"), communication cost is about ``O(2 * #feature * #bin)`` (check cost of "All Reduce" in chapter 4.5 at `[9] <#references>`__).
1. Instead of "Merge global histograms from all local histograms", LightGBM uses "Reduce Scatter" to merge histograms of different (non-overlapping) features for different workers.
[2] Mehta, Manish, Rakesh Agrawal, and Jorma Rissanen. "SLIQ: A fast scalable classifier for data mining." International Conference on Extending Database Technology. Springer Berlin Heidelberg, 1996.
[3] Shafer, John, Rakesh Agrawal, and Manish Mehta. "SPRINT: A scalable parallel classifier for data mining." Proc. 1996 Int. Conf. Very Large Data Bases. 1996.
[4] Ranka, Sanjay, and V. Singh. "CLOUDS: A decision tree classifier for large datasets." Proceedings of the 4th Knowledge Discovery and Data Mining Conference. 1998.
[6] Li, Ping, Qiang Wu, and Christopher J. Burges. "Mcrank: Learning to rank using multiple classification and gradient boosting." Advances in Neural Information Processing Systems 20 (NIPS 2007).
[8] Walter D. Fisher. "`On Grouping for Maximum Homogeneity`_." Journal of the American Statistical Association. Vol. 53, No. 284 (Dec., 1958), pp. 789-798.
[9] Thakur, Rajeev, Rolf Rabenseifner, and William Gropp. "`Optimization of collective communication operations in MPICH`_." International Journal of High Performance Computing Applications 19.1 (2005), pp. 49-66.
