feat: add divisive shapley (#1)

opensv/divisive_shapley/divisive_shapley.py

@@ -0,0 +1,52 @@
+from typing import List, Callable, Tuple
+import numpy as np
+from sklearn.cluster import KMeans
+
+"""
+References:
+[1] Shapley Value Approximation with Divisive Clustering
+[2] Shapley Values for dependent features using Divisive Clustering
+"""
+
+
+def shapley_value_exact(S: np.ndarray, v: Callable[[np.ndarray], float]) -> np.ndarray:
+    # Placeholder for exact Shapley value calculation
+    # Implement the actual Shapley value computation for coalition S
+    return np.random.rand(len(S))
+
+
+def characteristic_function(S: np.ndarray) -> float:
+    # Placeholder for characteristic function
+    return np.sum(S)  # Example: sum of values
+
+
+class DivisiveShapley:
+    def __init__(self, beta: float):
+        self.beta = beta
+
+    def divisive_shap_approx(self, S: np.ndarray, v: Callable[[np.ndarray], float]) -> np.ndarray:
+        n = len(S)
+        if n <= np.log(n) / np.log(self.beta):
+            return shapley_value_exact(S, v)
+        else:
+            kmeans = KMeans(n_clusters=2, random_state=0).fit(S.reshape(-1, 1))
+            labels = kmeans.labels_
+            unique_labels = np.unique(labels)
+            shap_values = np.zeros(n)
+
+            for label in unique_labels:
+                subcoalition = S[labels == label]
+                shap_values[labels == label] = self.divisive_shap_approx(subcoalition, v)
+
+            # Synergy adjustments could be made here if necessary
+            return shap_values
+
+    def calculate(self, N: np.ndarray, v: Callable[[np.ndarray], float]) -> np.ndarray:
+        return self.divisive_shap_approx(N, v)
+
+
+# Usage Example
+N = np.random.rand(100)  # Example data
+div_shap = DivisiveShapley(beta=2)
+shapley_values = div_shap.calculate(N, characteristic_function)
+print(shapley_values)