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Tree Methods

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############ Tree Methods ############

For training boosted tree models, there are 2 parameters used for choosing algorithms, namely updater and tree_method. XGBoost has 3 builtin tree methods, namely exact, approx and hist. Along with these tree methods, there are also some free standing updaters including refresh, prune and sync. The parameter updater is more primitive than tree_method as the latter is just a pre-configuration of the former. The difference is mostly due to historical reasons that each updater requires some specific configurations and might have missing features. As we are moving forward, the gap between them is becoming more and more irrelevant. We will collectively document them under tree methods.

Exact Solution

Exact means XGBoost considers all candidates from data for tree splitting, but underlying the objective is still interpreted as a Taylor expansion.

  1. exact: The vanilla gradient boosting tree algorithm described in reference paper <http://arxiv.org/abs/1603.02754>_. During split-finding, it iterates over all entries of input data. It's more accurate (among other greedy methods) but computationally slower in compared to other tree methods. Further more, its feature set is limited. Features like distributed training and external memory that require approximated quantiles are not supported. This tree method can be used with the parameter tree_method set to exact.

Approximated Solutions

As exact tree method is slow in computation performance and difficult to scale, we often employ approximated training algorithms. These algorithms build a gradient histogram for each node and iterate through the histogram instead of real dataset. Here we introduce the implementations in XGBoost.

  1. approx tree method: An approximation tree method described in reference paper <http://arxiv.org/abs/1603.02754>_. It runs sketching before building each tree using all the rows (rows belonging to the root). Hessian is used as weights during sketch. The algorithm can be accessed by setting tree_method to approx.

  2. hist tree method: An approximation tree method used in LightGBM with slight differences in implementation. It runs sketching before training using only user provided weights instead of hessian. The subsequent per-node histogram is built upon this global sketch. This is the fastest algorithm as it runs sketching only once. The algorithm can be accessed by setting tree_method to hist.

Implications

Some objectives like reg:squarederror have constant hessian. In this case, the hist should be preferred as weighted sketching doesn't make sense with constant weights. When using non-constant hessian objectives, sometimes approx yields better accuracy, but with slower computation performance. Most of the time using hist with higher max_bin can achieve similar or even superior accuracy while maintaining good performance. However, as xgboost is largely driven by community effort, the actual implementations have some differences than pure math description. Result might be slightly different than expectation, which we are currently trying to overcome.

Other Updaters

  1. Prune: It prunes the existing trees. prune is usually used as part of other tree methods. To use pruner independently, one needs to set the process type to update by: {"process_type": "update", "updater": "prune"}. With this set of parameters, during training, XGBoost will prune the existing trees according to 2 parameters min_split_loss (gamma) and max_depth.

  2. Refresh: Refresh the statistic of built trees on a new training dataset. Like the pruner, To use refresh independently, one needs to set the process type to update: {"process_type": "update", "updater": "refresh"}. During training, the updater will change statistics like cover and weight according to the new training dataset. When refresh_leaf is also set to true (default), XGBoost will update the leaf value according to the new leaf weight, but the tree structure (split condition) itself doesn't change.

    There are examples on both training continuation (adding new trees) and using update process on demo/guide-python. Also checkout the process_type parameter in :doc:parameter.

  3. Sync: Synchronize the tree among workers when running distributed training.

Removed Updaters

3 Updaters were removed during development due to maintainability. We describe them here solely for the interest of documentation.

  1. Distributed colmaker, which was a distributed version of exact tree method. It required specialization for column based splitting strategy and a different prediction procedure. As the exact tree method is slow by itself and scaling is even less efficient, we removed it entirely.

  2. skmaker. Per-node weighted sketching employed by grow_local_histmaker is slow, the skmaker was unmaintained and seems to be a workaround trying to eliminate the histogram creation step and uses sketching values directly during split evaluation. It was never tested and contained some unknown bugs, we decided to remove it and focus our resources on more promising algorithms instead. For accuracy, most of the time approx and hist are enough with some parameters tuning, so removing them don't have any real practical impact.

  3. grow_local_histmaker updater: An approximation tree method described in reference paper <http://arxiv.org/abs/1603.02754>_. This updater was rarely used in practice so it was still an updater rather than tree method. During split finding, it first runs a weighted GK sketching for data points belong to current node to find split candidates, using hessian as weights. The histogram is built upon this per-node sketch. It was faster than exact in some applications, but still slow in computation. It was removed because it depended on Rabit's customized reduction function that handles all the data structure that can be serialized/deserialized into fixed size buffer, which is not directly supported by NCCL or federated learning gRPC, making it hard to refactor into a common allreducer interface.

Feature Matrix

Following table summarizes some differences in supported features between 4 tree methods, T means supported while F means unsupported.

+------------------+-----------+---------------------+------------------------+------------------------+ | | Exact | Approx | Approx (GPU) | Hist | +==================+===========+=====================+========================+========================+ | grow_policy | Depthwise | depthwise/lossguide | depthwise/lossguide | depthwise/lossguide | +------------------+-----------+---------------------+------------------------+------------------------+ | max_leaves | F | T | T | T | +------------------+-----------+---------------------+------------------------+------------------------+ | sampling method | uniform | uniform | gradient_based/uniform | gradient_based/uniform | +------------------+-----------+---------------------+------------------------+------------------------+ | categorical data | F | T | T | T | +------------------+-----------+---------------------+------------------------+------------------------+ | External memory | F | T | P | T | +------------------+-----------+---------------------+------------------------+------------------------+ | Distributed | F | T | T | T | +------------------+-----------+---------------------+------------------------+------------------------+

Features/parameters that are not mentioned here are universally supported for all 3 tree methods (for instance, column sampling and constraints). The P in external memory means special handling. Please note that both categorical data and external memory are experimental.