331 adding faith banzhaf approximator (#333)

* Added FBII

* Introduces game normalization for FBII in exact.

* Added FBII to MC_Approximator

* Added FBI to Tabular Explainer

* Update regression coefficient calculation for FBII & FSII.

* refactoring of regression weight calculation

* fix fbii exact computation missing baseline_value addition

* Added FBII

* Introduces game normalization for FBII in exact.

* Added FBII to MC_Approximator

* Added FBI to Tabular Explainer

* Update regression coefficient calculation for FBII & FSII.

* refactoring of regression weight calculation

* fix fbii exact computation missing baseline_value addition

* updated regression_coefficient calculation

* improving approximation finalize result

* Consistent baseline/empty player value throughout InteractionValues.

* Sampling weight initialisation for FBII and corresponding approximation

* renamed finalize function

* finalized explanations for TreeExplainer

---------

Co-authored-by: Maximilian <maximilian.muschalik@gmail.com>

Author: Advueu963

CHANGELOG.md

@@ -6,6 +6,8 @@
 - fixes a bug with xgboost where feature names where trees that did not contain all features would lead `TreeExplainer` to fail
 - fixes a bug with `stacked_bar_plot` where the higher order interactions were inflated by the lower order interactions, thus wrongly showing the higher order interactions as higher than they are
 - fixes a bug where `InteractionValues.get_subset()` returns a faulty `coalition_lookup` dictionary pointing to indices outside the subset of players [#336](https://github.com/mmschlk/shapiq/issues/336)
+- updates default value of `TreeExplainer`'s `min_order` parameter from 1 to 0 to include the baseline value in the interaction values as per default
+- adds the `RegressionFBII` approximator to estimate Faithful Banzhaf interactions via least squares regression [#333](https://github.com/mmschlk/shapiq/pull/333). Additionally, FBII support was introduced in TabularExplainer and MonteCarlo-Approximator.
 
 ### v1.2.2 (2025-03-11)
 - changes python support to 3.10-3.13 [#318](https://github.com/mmschlk/shapiq/pull/318)

shapiq/approximator/__init__.py

@@ -6,7 +6,14 @@
 from .permutation.sii import PermutationSamplingSII
 from .permutation.stii import PermutationSamplingSTII
 from .permutation.sv import PermutationSamplingSV
-from .regression import InconsistentKernelSHAPIQ, KernelSHAP, KernelSHAPIQ, RegressionFSII, kADDSHAP
+from .regression import (
+    InconsistentKernelSHAPIQ,
+    KernelSHAP,
+    KernelSHAPIQ,
+    RegressionFBII,
+    RegressionFSII,
+    kADDSHAP,
+)
 
 # contains all SV approximators
 SV_APPROXIMATORS: list[Approximator.__class__] = [
@@ -57,6 +64,11 @@
     SHAPIQ,
 ]
 
+# contains all approximators that can be used for FBII
+FBII_APPROXIMATORS: list[Approximator.__class__] = [
+    RegressionFBII,
+]
+
 __all__ = [
     "PermutationSamplingSII",
     "PermutationSamplingSTII",
@@ -77,6 +89,7 @@
     "SII_APPROXIMATORS",
     "STII_APPROXIMATORS",
     "FSII_APPROXIMATORS",
+    "FBII_APPROXIMATORS",
 ]
 
 # Path: shapiq/approximator/__init__.py

shapiq/approximator/_base.py

@@ -1,17 +1,16 @@
 """This module contains the base approximator classes for the shapiq package."""
 
-import copy
+import warnings
 from abc import ABC, abstractmethod
 from collections.abc import Callable
 
 import numpy as np
+from scipy.special import binom
 
 from ..approximator.sampling import CoalitionSampler
 from ..game_theory.indices import (
     AVAILABLE_INDICES_FOR_APPROXIMATION,
     get_computation_index,
-    is_empty_value_the_baseline,
-    is_index_aggregated,
 )
 from ..interaction_values import InteractionValues
 from ..utils.sets import generate_interaction_lookup
@@ -143,13 +142,29 @@ def _init_sampling_weights(self) -> np.ndarray:
             The weights for sampling subsets of size ``s`` in shape ``(n + 1,)``.
         """
         weight_vector = np.zeros(shape=self.n + 1)
-        for coalition_size in range(0, self.n + 1):
-            if (coalition_size < self.max_order) or (coalition_size > self.n - self.max_order):
-                # prioritize these subsets
-                weight_vector[coalition_size] = self._big_M
-            else:
-                # KernelSHAP sampling weights
-                weight_vector[coalition_size] = 1 / (coalition_size * (self.n - coalition_size))
+        if self.index in ["FBII"]:
+
+            try:
+                for coalition_size in range(0, self.n + 1):
+                    weight_vector[coalition_size] = binom(self.n, coalition_size) / 2**self.n
+            except OverflowError:
+                for coalition_size in range(0, self.n + 1):
+                    weight_vector[coalition_size] = (
+                        1
+                        / np.sqrt(2 * np.pi * 0.5)
+                        * np.exp(-(coalition_size - self.n / 2) * +2 / (self.n / 2))
+                    )
+                warnings.warn(
+                    "The weights are approximated for n > 1000. While this is very close to the truth for sets for size in the region n/2, the approximation is not exact for size n or 0."
+                )
+        else:
+            for coalition_size in range(0, self.n + 1):
+                if (coalition_size < self.max_order) or (coalition_size > self.n - self.max_order):
+                    # prioritize these subsets
+                    weight_vector[coalition_size] = self._big_M
+                else:
+                    # KernelSHAP sampling weights
+                    weight_vector[coalition_size] = 1 / (coalition_size * (self.n - coalition_size))
         sampling_weight = weight_vector / np.sum(weight_vector)
         return sampling_weight
 
@@ -175,61 +190,6 @@ def _order_iterator(self) -> range:
         """
         return range(self.min_order, self.max_order + 1)
 
-    def _finalize_result(
-        self,
-        result,
-        baseline_value: float,
-        *,
-        estimated: bool | None = None,
-        budget: int | None = None,
-    ) -> InteractionValues:
-        """Finalizes the result dictionary.
-
-        Args:
-            result: Interaction values.
-            baseline_value: Baseline value.
-            estimated: Whether interaction values were estimated.
-            budget: The budget for the approximation.
-
-        Returns:
-            The interaction values.
-
-        Raises:
-            ValueError: If the baseline value is not provided for SII and k-SII.
-        """
-
-        if budget is None:  # try to get budget from sampler (exclude from coverage)
-            budget = self._sampler.n_coalitions  # pragma: no cover
-
-        if estimated is None:
-            estimated = False if budget >= 2**self.n else True
-
-        # set empty value as baseline value if necessary
-        if tuple() in self._interaction_lookup:
-            idx = self._interaction_lookup[tuple()]
-            empty_value = result[idx]
-            # only for SII empty value is not the baseline value
-            if empty_value != baseline_value and is_empty_value_the_baseline(self.index):
-                result[idx] = baseline_value
-
-        interactions = InteractionValues(
-            values=result,
-            estimated=estimated,
-            estimation_budget=budget,
-            index=self.approximation_index,  # can be different from self.index
-            min_order=self.min_order,
-            max_order=self.max_order,
-            n_players=self.n,
-            interaction_lookup=copy.deepcopy(self.interaction_lookup),
-            baseline_value=baseline_value,
-        )
-
-        # if index needs to be aggregated
-        if is_index_aggregated(self.index):
-            interactions = self.aggregate_interaction_values(interactions)
-
-        return interactions
-
     @staticmethod
     def _calc_iteration_count(budget: int, batch_size: int, iteration_cost: int) -> tuple[int, int]:
         """Computes the number of iterations and the size of the last batch given the batch size and
@@ -313,6 +273,6 @@ def aggregate_interaction_values(
         Returns:
             The aggregated interaction values.
         """
-        from shapiq.game_theory.aggregation import aggregate_interaction_values
+        from shapiq.game_theory.aggregation import aggregate_base_interaction
 
-        return aggregate_interaction_values(base_interactions, order=order)
+        return aggregate_base_interaction(base_interactions, order=order)

shapiq/approximator/marginals/owen.py

@@ -6,7 +6,7 @@
 
 import numpy as np
 
-from ...interaction_values import InteractionValues
+from ...interaction_values import InteractionValues, finalize_computed_interactions
 from .._base import Approximator
 
 
@@ -101,8 +101,21 @@ def approximate(
             idx = self._interaction_lookup[(player,)]
             result_to_finalize[idx] = result[player]
 
-        return self._finalize_result(
-            result_to_finalize, baseline_value=empty_value, budget=used_budget, estimated=True
+        interaction = InteractionValues(
+            n_players=self.n,
+            values=result_to_finalize,
+            index=self.approximation_index,
+            interaction_lookup=self._interaction_lookup,
+            baseline_value=empty_value,
+            min_order=self.min_order,
+            max_order=self.max_order,
+            estimated=True,
+            estimation_budget=used_budget,
+        )
+
+        return finalize_computed_interactions(
+            interaction,
+            target_index=self.index,
         )
 
     @staticmethod

shapiq/approximator/marginals/stratified.py

@@ -4,7 +4,7 @@
 
 import numpy as np
 
-from ...interaction_values import InteractionValues
+from ...interaction_values import InteractionValues, finalize_computed_interactions
 from .._base import Approximator
 
 
@@ -37,13 +37,14 @@ def __init__(
         self.iteration_cost: int = 2
 
     def approximate(
-        self, budget: int, game: Callable[[np.ndarray], np.ndarray]
+        self, budget: int, game: Callable[[np.ndarray], np.ndarray], *args, **kwargs
     ) -> InteractionValues:
         """Approximates the Shapley values using ApproShapley.
 
         Args:
             budget: The number of game evaluations for approximation
             game: The game function as a callable that takes a set of players and returns the value.
+            *args and **kwargs: Additional arguments not used.
 
         Returns:
             The estimated interaction values.
@@ -114,6 +115,16 @@ def approximate(
             idx = self._interaction_lookup[(player,)]
             result_to_finalize[idx] = result[player]
 
-        return self._finalize_result(
-            result_to_finalize, baseline_value=empty_value, budget=used_budget, estimated=True
+        interactions = InteractionValues(
+            n_players=self.n,
+            values=result_to_finalize,
+            index=self.approximation_index,
+            interaction_lookup=self._interaction_lookup,
+            baseline_value=float(empty_value),
+            min_order=self.min_order,
+            max_order=self.max_order,
+            estimated=True,
+            estimation_budget=used_budget,
         )
+
+        return finalize_computed_interactions(interactions, target_index=self.index)

shapiq/approximator/montecarlo/_base.py

@@ -6,7 +6,7 @@
 from scipy.special import binom, factorial
 
 from ...game_theory.indices import AVAILABLE_INDICES_MONTE_CARLO
-from ...interaction_values import InteractionValues
+from ...interaction_values import InteractionValues, finalize_computed_interactions
 from ...utils.sets import powerset
 from .._base import Approximator
 
@@ -50,7 +50,7 @@ def __init__(
                 f"Index {index} not available for Regression Approximator. Choose from "
                 f"{AVAILABLE_INDICES_MONTE_CARLO}."
             )
-        if index == "FSII":
+        if index in ["FSII", "FBII"]:
             top_order = True
         super().__init__(
             n,
@@ -99,10 +99,20 @@ def approximate(
 
         baseline_value = float(game_values[self._sampler.empty_coalition_index])
 
-        return self._finalize_result(
-            result=shapley_interactions_values, baseline_value=baseline_value, budget=budget
+        interactions = InteractionValues(
+            shapley_interactions_values,
+            index=self.approximation_index,
+            n_players=self.n,
+            interaction_lookup=self.interaction_lookup,
+            min_order=self.min_order,
+            max_order=self.max_order,
+            baseline_value=baseline_value,
+            estimated=False if budget >= 2**self.n else True,
+            estimation_budget=budget,
         )
 
+        return finalize_computed_interactions(interactions, target_index=self.index)
+
     def monte_carlo_routine(
         self,
         game_values: np.ndarray,
@@ -386,8 +396,7 @@ def _stii_weight(self, coalition_size: int, interaction_size: int) -> float:
         """
         if interaction_size == self.max_order:
             return self.max_order / (self.n * binom(self.n - 1, coalition_size))
-        else:
-            return 1.0 * (coalition_size == 0)
+        return 1.0 * (coalition_size == 0)
 
     def _fsii_weight(self, coalition_size: int, interaction_size: int) -> float:
         """Returns the FSII discrete derivative weight given the coalition size and interaction
@@ -411,8 +420,24 @@ def _fsii_weight(self, coalition_size: int, interaction_size: int) -> float:
                 * factorial(coalition_size + self.max_order - 1)
                 / factorial(self.n + self.max_order - 1)
             )
-        else:
-            raise ValueError("Lower order interactions are not supported.")
+        raise ValueError(f"Lower order interactions are not supported for {self.index}.")
+
+    def _fbii_weight(self, interaction_size: int) -> float:
+        """Returns the FSII discrete derivative weight given the coalition size and interaction
+        size.
+
+        The representation is based on the FBII representation according to Theorem 17 by
+        `Tsai et al. (2023) <https://doi.org/10.48550/arXiv.2203.00870>`_.
+
+        Args:
+            interaction_size: The size of the interaction.
+
+        Returns:
+            The weight for the interaction type.
+        """
+        if interaction_size == self.max_order:
+            return 1 / 2 ** (self.n - interaction_size)
+        raise ValueError(f"Lower order interactions are not supported for {self.index}.")
 
     def _weight(self, index: str, coalition_size: int, interaction_size: int) -> float:
         """Returns the weight for each interaction type given coalition and interaction size.
@@ -429,6 +454,8 @@ def _weight(self, index: str, coalition_size: int, interaction_size: int) -> flo
             return self._stii_weight(coalition_size, interaction_size)
         elif index == "FSII":
             return self._fsii_weight(coalition_size, interaction_size)
+        elif index == "FBII":
+            return self._fbii_weight(interaction_size)
         elif index in ["SII", "SV"]:
             return self._sii_weight(coalition_size, interaction_size)
         elif index == "BII":

shapiq/approximator/permutation/sii.py

@@ -4,7 +4,7 @@
 
 import numpy as np
 
-from ...interaction_values import InteractionValues
+from ...interaction_values import InteractionValues, finalize_computed_interactions
 from ...utils.sets import powerset
 from .._base import Approximator
 
@@ -143,6 +143,16 @@ def approximate(
         # compute mean of interactions
         result = np.divide(result, counts, out=result, where=counts != 0)
 
-        return self._finalize_result(
-            result, baseline_value=empty_value, budget=used_budget, estimated=True
+        interactions = InteractionValues(
+            n_players=self.n,
+            values=result,
+            index=self.approximation_index,
+            interaction_lookup=self._interaction_lookup,
+            baseline_value=empty_value,
+            min_order=self.min_order,
+            max_order=self.max_order,
+            estimated=True,
+            estimation_budget=used_budget,
         )
+
+        return finalize_computed_interactions(interactions, target_index=self.index)