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import numpy as np # For arithmetics and arrays
import math # For inbuilt math functions
import pandas as pd # For handling data frames
import collections # used for dictionaries and counters
from itertools import permutations # used to find permutations
from sklearn.ensemble import GradientBoostingClassifier
from sklearn.ensemble import RandomForestClassifier
from sklearn.tree import DecisionTreeClassifier # Import Decision Tree Classifier
from sklearn.model_selection import train_test_split # Import train_test_split function to easily split data into training and testing samples
from sklearn.decomposition import PCA # Principal component analysis used to reduce the number of features in a model
from sklearn.preprocessing import StandardScaler # used to scale data to be used in the model
from sklearn import metrics #Import scikit-learn metrics module for accuracy calculation
from sklearn.metrics import confusion_matrix
from sklearn.metrics import classification_report
from sklearn.metrics import roc_auc_score
from sklearn.metrics import roc_curve
from sklearn.metrics import accuracy_score
from sklearn.metrics import log_loss
import pickle # To save the trained model and then read it
import seaborn as sns # Create plots
import matplotlib.pyplot as plt
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