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Hoeffding Adaptive Tree regressor (HATR).

This class implements a regression version of the Hoeffding Adaptive Tree Classifier. Hence, it also uses an ADWIN concept-drift detector instance at each decision node to monitor possible changes in the data distribution. If a drift is detected in a node, an alternate tree begins to be induced in the background. When enough information is gathered, HATR swaps the node where the change was detected by its alternate tree.


  • grace_period (int) – defaults to 200

    Number of instances a leaf should observe between split attempts.

  • max_depth (int) – defaults to None

    The maximum depth a tree can reach. If None, the tree will grow indefinitely.

  • delta (float) – defaults to 1e-07

    Significance level to calculate the Hoeffding bound. The significance level is given by 1 - delta. Values closer to zero imply longer split decision delays.

  • tau (float) – defaults to 0.05

    Threshold below which a split will be forced to break ties.

  • leaf_prediction (str) – defaults to adaptive

    Prediction mechanism used at leafs.
    - 'mean' - Target mean
    - 'model' - Uses the model defined in leaf_model
    - 'adaptive' - Chooses between 'mean' and 'model' dynamically

  • leaf_model (base.Regressor) – defaults to None

    The regression model used to provide responses if leaf_prediction='model'. If not provided an instance of river.linear_model.LinearRegression with the default hyperparameters is used.

  • model_selector_decay (float) – defaults to 0.95

    The exponential decaying factor applied to the learning models' squared errors, that are monitored if leaf_prediction='adaptive'. Must be between 0 and 1. The closer to 1, the more importance is going to be given to past observations. On the other hand, if its value approaches 0, the recent observed errors are going to have more influence on the final decision.

  • nominal_attributes (list) – defaults to None

    List of Nominal attributes. If empty, then assume that all numeric attributes should be treated as continuous.

  • splitter (river.tree.splitter.base.Splitter) – defaults to None

    The Splitter or Attribute Observer (AO) used to monitor the class statistics of numeric features and perform splits. Splitters are available in the tree.splitter module. Different splitters are available for classification and regression tasks. Classification and regression splitters can be distinguished by their property is_target_class. This is an advanced option. Special care must be taken when choosing different splitters. By default, tree.splitter.TEBSTSplitter is used if splitter is None.

  • min_samples_split (int) – defaults to 5

    The minimum number of samples every branch resulting from a split candidate must have to be considered valid.

  • bootstrap_sampling (bool) – defaults to True

    If True, perform bootstrap sampling in the leaf nodes.

  • drift_window_threshold (int) – defaults to 300

    Minimum number of examples an alternate tree must observe before being considered as a potential replacement to the current one.

  • drift_detector (Optional[base.DriftDetector]) – defaults to None

    The drift detector used to build the tree. If None then drift.ADWIN is used. Only detectors that support arbitrarily valued continuous data can be used for regression.

  • switch_significance (float) – defaults to 0.05

    The significance level to assess whether alternate subtrees are significantly better than their main subtree counterparts.

  • binary_split (bool) – defaults to False

    If True, only allow binary splits.

  • max_size (float) – defaults to 500.0

    The max size of the tree, in Megabytes (MB).

  • memory_estimate_period (int) – defaults to 1000000

    Interval (number of processed instances) between memory consumption checks.

  • stop_mem_management (bool) – defaults to False

    If True, stop growing as soon as memory limit is hit.

  • remove_poor_attrs (bool) – defaults to False

    If True, disable poor attributes to reduce memory usage.

  • merit_preprune (bool) – defaults to True

    If True, enable merit-based tree pre-pruning.

  • seed (int) – defaults to None

    Random seed for reproducibility.


  • height

  • leaf_prediction

    Return the prediction strategy used by the tree at its leaves.

  • max_size

    Max allowed size tree can reach (in MB).

  • n_active_leaves

  • n_alternate_trees

  • n_branches

  • n_inactive_leaves

  • n_leaves

  • n_nodes

  • n_pruned_alternate_trees

  • n_switch_alternate_trees

  • split_criterion

    Return a string with the name of the split criterion being used by the tree.

  • summary

    Collect metrics corresponding to the current status of the tree in a string buffer.


>>> from river import datasets
>>> from river import evaluate
>>> from river import metrics
>>> from river import tree
>>> from river import preprocessing

>>> dataset = datasets.TrumpApproval()

>>> model = (
...     preprocessing.StandardScaler() |
...     tree.HoeffdingAdaptiveTreeRegressor(
...         grace_period=50,
...         model_selector_decay=0.3,
...         seed=0
...     )
... )

>>> metric = metrics.MAE()

>>> evaluate.progressive_val_score(dataset, model, metric)
MAE: 0.809874



Print an explanation of how x is predicted.


  • x (dict)


typing.Optional[str]: A representation of the path followed by the tree to predict x; None if


Draw the tree using the graphviz library.

Since the tree is drawn without passing incoming samples, classification trees will show the majority class in their leaves, whereas regression trees will use the target mean.


  • max_depth (int) – defaults to None
    The maximum depth a tree can reach. If None, the tree will grow indefinitely.

Train the tree model on sample x and corresponding target y.


  • x
  • y
  • sample_weight – defaults to 1.0




Predict the target value using one of the leaf prediction strategies.


  • x


Predicted target value.


Return a representation of the current tree structure organized in a pandas.DataFrame object.

In case the tree is empty or it only contains a single node (a leaf), None is returned.




The Hoeffding Adaptive Tree 1 uses drift detectors to monitor performance of branches in the tree and to replace them with new branches when their accuracy decreases.

The bootstrap sampling strategy is an improvement over the original Hoeffding Adaptive Tree algorithm. It is enabled by default since, in general, it results in better performance.

To cope with ADWIN's requirements of bounded input data, HATR uses a novel error normalization strategy based on the empiral rule of Gaussian distributions. We assume the deviations of the predictions from the expected values follow a normal distribution. Hence, we subject these errors to a min-max normalization assuming that most of the data lies in the \(\left[-3\sigma, 3\sigma\right]\) range. These normalized errors are passed to the ADWIN instances. This is the same strategy used by Adaptive Random Forest Regressor.


  1. Bifet, Albert, and Ricard GavaldΓ . "Adaptive learning from evolving data streams." In International Symposium on Intelligent Data Analysis, pp. 249-260. Springer, Berlin, Heidelberg, 2009.