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 (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.

• split_confidence (float) – defaults to 1e-07

Allowed error in split decision, a value closer to 0 takes longer to decide.

• tie_threshold (float) – defaults to 0.05

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

• leaf_prediction (str) – defaults to model

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.EBSTSplitter 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.

• adwin_confidence (float) – defaults to 0.002

The delta parameter used in the nodes' ADWIN drift detectors.

• binary_split (bool) – defaults to False

If True, only allow binary splits.

• max_size (int) – defaults to 100

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 – defaults to None

If int, seed is the seed used by the random number generator;
If RandomState instance, seed is the random number generator;
If None, the random number generator is the RandomState instance used by np.random. Only used when bootstrap_sampling=True to direct the bootstrap sampling.

## Attributes¶

• 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.

## 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() |
...         grace_period=50,
...         model_selector_decay=0.3,
...         seed=0
...     )
... )

>>> metric = metrics.MAE()

>>> evaluate.progressive_val_score(dataset, model, metric)
MAE: 0.78838


## Methods¶

clone

Return a fresh estimator with the same parameters.

The clone has the same parameters but has not been updated with any data. This works by looking at the parameters from the class signature. Each parameter is either - recursively cloned if it's a River classes. - deep-copied via copy.deepcopy if not. If the calling object is stochastic (i.e. it accepts a seed parameter) and has not been seeded, then the clone will not be idempotent. Indeed, this method's purpose if simply to return a new instance with the same input parameters.

debug_one

Print an explanation of how x is predicted.

Parameters

• x (dict)

Returns

typing.Union[str, NoneType]: 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) – defaults to None
The maximum depth a tree can reach. If None, the tree will grow indefinitely.
learn_one

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

Parameters

• x
• y
• sample_weight – defaults to 1.0

Returns

self

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 ADWIN 2 to monitor performance of branches on the tree and to replace them with new branches when their accuracy decreases if the new branches are more accurate.

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.

## References¶

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.

2. Bifet, Albert, and Ricard Gavaldà. "Learning from time-changing data with adaptive windowing." In Proceedings of the 2007 SIAM international conference on data mining, pp. 443-448. Society for Industrial and Applied Mathematics, 2007.