HoeffdingAdaptiveTreeRegressor

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.

Parameters

• grace_period

  Type → int

  Default → 200

  Number of instances a leaf should observe between split attempts.

• max_depth

  Type → int | None

  Default → None

  The maximum depth a tree can reach. If None, the tree will grow until the system recursion limit.

• delta

  Type → float

  Default → 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

  Type → float

  Default → 0.05

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

• leaf_prediction

  Type → str

  Default → 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

  Type → base.Regressor | None

  Default → None

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

• model_selector_decay

  Type → float

  Default → 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

  Type → list | None

  Default → None

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

• splitter

  Type → Splitter | None

  Default → 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

  Type → int

  Default → 5

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

• bootstrap_sampling

  Type → bool

  Default → True

  If True, perform bootstrap sampling in the leaf nodes.

• drift_window_threshold

  Type → int

  Default → 300

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

• drift_detector

  Type → base.DriftDetector | None

  Default → 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

  Type → float

  Default → 0.05

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

• binary_split

  Type → bool

  Default → False

  If True, only allow binary splits.

• max_size

  Type → float

  Default → 500.0

  The max size of the tree, in mebibytes (MiB).

• memory_estimate_period

  Type → int

  Default → 1000000

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

• stop_mem_management

  Type → bool

  Default → False

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

• remove_poor_attrs

  Type → bool

  Default → False

  If True, disable poor attributes to reduce memory usage.

• merit_preprune

  Type → bool

  Default → True

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

• seed

  Type → int | None

  Default → None

  Random seed for reproducibility.

Attributes

• height

• leaf_prediction

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

• max_size

  Max allowed size tree can reach (in MiB).

• 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.

Examples

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: 0.917576

Methods

debug_one

Print an explanation of how x is predicted.

Parameters

• x — 'dict'

Returns

str | None: A representation of the path followed by the tree to predict x; None if

draw

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.

Parameters

• max_depth — 'int | None' — defaults to None
  The maximum depth a tree can reach. If None, the tree will grow until the system recursion limit.

learn_one

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

Parameters

• x
• y
• w — defaults to 1.0

predict_one

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

Parameters

• x

Returns

Predicted target value.

to_dataframe

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.

Returns

df

Notes

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.

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