Normalized Movement Rate (NMR) is a proxy that examines the stability of any XAI method when generating list of most informative predictors. It tests how the order of the informative predictors will be chnaged when there is collinearity among the predictors. Its values ranges from 0 to 1. NMR = 1 means there is a sharp change in the order of the predictors when some features are iteratively removed from the model and accordingly the list is unstable.
To read more about the method and its implementation, see paper

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Implementing

The following example shows how to calculate NMR using LogisticRegression as machine learning model and SHAP as XAI method. If you use different machine learning model, then you have to change the model in the code and the explainer in SHAP.

import pandas as pd
import shap
from statistics import mean
from sklearn.linear_model import LogisticRegression
from numpy import mean
import numpy as np


X_train = path 
X_test  = path
y_train = path
y_test  = path
Columns_list = list(X_train.columns.values)
dicts = dict()
m = 0
MPM_list = []
while X_train.shape[1] != 1 :
    MPM = 0
    NF = X_train.shape[1]
    for j in range(1, NF, 2):
        summ = NF-j
        MPM = MPM+summ
    MPM = MPM*2
    MPM_list.append(MPM)
    #print('MPM :', MPM)
    
    #print('Iteration: ', X_train.shape[1])                          ## number of features in each iteration
    model= LogisticRegression(C=0.1)                                ## defin a model
    model.fit(X_train, y_train.values.ravel())                      ## fit the data to the model
    ypred_test = model.predict (X_test)                             ## predict test data
    
    #prepare the data for shap
    masker = shap.maskers.Independent(data = X_train)
    
    # fit shap
    explainer = shap.LinearExplainer(model, masker = masker)
    
    # apply shap to test data
    shap_values = explainer.shap_values(X_test)
    
    # the follwoing steps to represents the SHAP outcome (informative predictors) as datafram
    vals= np.abs(shap_values).mean(0)
    feature_importance = pd.DataFrame(list(zip(X_train.columns,vals)),columns=['Features','feature_importance_vals'])
    feature_importance.sort_values(by=['feature_importance_vals'],ascending=False,inplace=True)
    feature_importance.reset_index(inplace=True, drop=True)
    feature_importance.index = np.arange(1, len(feature_importance) + 1)
    #print(feature_importance)
    FEATURES = feature_importance[['Features']]
    #print(FEATURES)
    for i in range(FEATURES.shape[0]):
        #print(FEATURES.iloc[i]['Features'], end = " ")
        #print(FEATURES.iloc[i].name, end = " ")
        #for key in dicts:
        if FEATURES.iloc[i]['Features'] in dicts:
            dicts[FEATURES.iloc[i]['Features']].append(FEATURES.iloc[i].name + m)
        else:
            dicts[FEATURES.iloc[i]['Features']] = [FEATURES.iloc[i].name + m]
    
    m = m+1
    #print('\t')
    # identify the most informative predictor
    Top_feature = feature_importance.iloc[0]['Features']
    
    # remove the most informative predictor from train and test data
    X_train.drop([Top_feature], axis=1, inplace=True)
    X_train.reset_index(inplace=True, drop=True)
    X_test.drop([Top_feature], axis=1, inplace=True)
    X_test.reset_index(inplace=True, drop=True)
    #print('===================================================')
MPM_list.pop(0)

And finally calculate NMR

lenOfLists=len(dicts)
#function to add item at index=len ... append item
def add_item_to_dict(my_dict, key, value):
    my_dict[len(my_dict)] = [key,value]

    
sorted_dict = {}

for index in range(1,lenOfLists):
    for key, value in dicts.items():
        if len(value)==index:
            add_item_to_dict(sorted_dict,key,value)

#calculate sum of changes
sumOfChanges={}
#first is zero
add_item_to_dict(sumOfChanges,sorted_dict[0][0],0)

for index in range(1,lenOfLists-1):  
    key=sorted_dict[index][0]
    soc=0
    for t in range(index,lenOfLists):        
        soc+=abs(sorted_dict[t][1][index]-sorted_dict[t][1][index-1])
        #print(sorted_dict[t][1][index],sorted_dict[t][1][index-1],(sorted_dict[t][1][index]-sorted_dict[t][1][index-1]))
    add_item_to_dict(sumOfChanges,key,soc)
    #print(soc,'----') 
#last is same to last -1
add_item_to_dict(sumOfChanges,sorted_dict[lenOfLists-1][0],sumOfChanges[lenOfLists-2][1])
#print(sorted_dict)
#print(sumOfChanges)
sumOfChanges.popitem()
first_key = next(iter(sumOfChanges))
del sumOfChanges[first_key]
rates = []
ite=0
for key, value in sumOfChanges.items():    
    rates.append(value[1]/MPM_list[ite])
    ite=ite+1
#print(rates)
print("NMR value : ", round(mean(rates), 3))