Cartesian Partitions

CartesianTreePartition

Cartesian tree partition.
treehfd.cartesian_partition.CartesianTreePartition(main_variables: ndarray) → None

Cartesian tree partition.

This class defines the Cartesian tree partitions of a given tree from the splitting variables and values.

treehfd.cartesian_partition.main_variables

List of variable indices for main effects.

Type:

np.ndarray

treehfd.cartesian_partition.partition_index

Indices of all main effect partitions.

Type:

np.ndarray

treehfd.cartesian_partition.split_list

List of splitting values for all main effects.

Type:

list

treehfd.cartesian_partition.cell_list

List of array of cell indices for each component.

Type:

list

treehfd.cartesian_partition.counts_list

List of sizes of each cell of interaction partitions.

Type:

list

treehfd.cartesian_partition.CartesianTreePartition.compute_cartesian_partition(self, X: ndarray, tree_structure: tuple[ndarray, ndarray, ndarray], interaction_list: list[list[int]]) → ndarray

Compute Cartesian tree partitions from tree structure and data.

Parameters:

  • X (np.ndarray) – The input data used to train the xgboost model.

  • tree_structure (tuple) – Tuple containing the splitting variables, children node indices, and splitting values of the tree.

  • interaction_list (list) – List of variable index pairs, with a pair for each interaction.

Returns:

X_bin – Array with the cell indices of all Cartesian partitions for each training point.

Return type:

np.ndarray

treehfd.cartesian_partition.CartesianTreePartition.compute_partition_main(self, X: ndarray, variables: ndarray, split_values: ndarray) → ndarray

Compute Cartesian tree partitions of main effects.

Parameters:

  • X (np.ndarray) – The input data used to train the xgboost model.

  • variables (np.ndarray) – Array with the splitting variables of the tree.

  • split_values (np.ndarray) – Array with the splitting values of the tree.

Returns:

X_bin_main – Array with the cell indices of main-effect partitions for each training point.

Return type:

np.ndarray

treehfd.cartesian_partition.CartesianTreePartition.compute_partition_order2(self, X_bin_main: ndarray, interaction_list: list[list[int]]) → ndarray

Compute Cartesian tree partitions of second-order interactions.

Parameters:

  • X_bin_main (np.ndarray) – Array with the cell indices of main-effect partitions for each training point.

  • interaction_list (list) – List of variable index pairs, with a pair for each interaction.

Returns:

X_bin_order2 – Array with the cell indices of second-order partitions for each training point.

Return type:

np.ndarray

treehfd.cartesian_partition.CartesianTreePartition.predict_partition(self, X_new: ndarray, interaction_list: list[list[int]]) → tuple[ndarray, ndarray]

Predict cells of the Cartesian tree partitions for new input data.

Parameters:

  • X_new (np.ndarray) – New input data where TreeHFD predictions are computed.

  • interaction_list (list) – List of variable index pairs, with a pair for each interaction.

Returns:

X_bin_mainnp.ndarray

Array with the cell indices of main-effect partitions for the new input data.

X_bin_order2np.ndarray

Array with the cell indices of interaction partitions for the new input data.

Return type:

tuple