Added Cook's Distance

Author: megpay

maths/cooks_distance.py

@@ -0,0 +1,49 @@
+"""
+Cook's Distance is used to estimate the influence of a data point in 
+in least squares regression. 
+
+Cook's Distance removes each data point and measures the effect of removing the
+data point. 
+
+The algorithm works as follows:
+For each data point in the regression, remove the point from the set 
+    and calculate the effect of removing that point. 
+
+D_i = (sum over all other points(y_actual - y_observed)^2) / (rank * MSE^2) 
+
+
+https://en.wikipedia.org/wiki/Cook's_distance
+"""
+from machine_learning.loss_functions.mean_squared_error import mean_squared_error
+import numpy as np
+
+def calculate_cooks_distance(y_observed: array, y_fitted: array, rank: int) -> array:
+    """Calculate Cook's Distance
+        Input: 
+            y_observed: numpy array of observed y values
+            y_fitted: numpy array of fitted y values from linear regression model
+            rank: int representing the number of coefficients
+        Output:
+            cooks_distance: numpy array of Cook's distance for each y value.
+         
+    """
+    import numpy as np
+    _mse = mean_squared_error(y_observed, y_fitted)
+    _y_difference_squared = (y_observed - y_fitted)**2
+
+    if isinstance(rank) is not int:
+        msg = f"Rank is an integer representing the number of predictors. Input: {rank}"
+        raise TypeError(msg)
+    
+    if len(y_observed) != len(y_fitted):
+        msg = f"The arrays of observed and fitted values must be equal length. Currently 
+            observed = {len(y_observed)} and fitted = {len(y_fitted)}"
+        raise ValueError(msg)
+
+    if len(y_observed) == 0:
+        raise ValueError("The y value arrays must not be empty")
+
+    _summed_difference = sum(_y_difference_squared)
+    for item in np.nditer(_y_difference_squared):
+        k = (_summed_difference - item) / (rank * _mse)
+