Revisions to Why my R^2 for my cross validation decreases as the polynomial degree increases?

deleted 164 characters in body

Source Link

edited Aug 11, 2022 at 16:55

31
6

from sklearn.model_selection import cross_val_score
    from sklearn.model_selection import KFold
    from sklearn.metrics import r2_score
    
crossvalidation_poly = KFold(n_splits=3, shuffle=True) # Why are we using kfold=3 not 10; Because if you choose k=10, then you are increasing the points in validation set, so you are "using less data" to train the model

#for train_index, test_index in crossvalidation_poly.split(X_normalized):


for i in range(1,11):
    poly_cross_validation = PolynomialFeatures(degree=i)
    X_current = poly.fit_transform(X_normalized)
    model = lin_regressor.fit(X_current, y_for_normalized)
    scores = cross_val_score(model, X_current,y_for_normalized, scoring='r2', cv=crossvalidation_poly,
 n_jobs=1)
    

    print("\n\nDegree-"+str(i) +" polynomial: R^2 for every fold: " + str(np.abs(scores)))
          
          #+" training: " + str(np.abs(train_index))+" \ntesting: " + str(np.abs(test_index)))

    print('\033[1m'+"Degree-"+str(i)+ '\033[1m'+ " polynomial: Average R^2 for all the folds: " + str(np.mean(np.abs(scores))) + '\033[0m'+ ", STD: " + str(np.std(scores)))


Degree-1 polynomial: R^2 for every fold: [0.41300831 0.45801624 0.17011995]
Degree-1 polynomial: Average R^2 for all the folds: 0.34704816498535956, STD: 0.2860884371794798


Degree-2 polynomial: R^2 for every fold: [0.75123033 0.85035531 0.40642591]
Degree-2 polynomial: Average R^2 for all the folds: 0.6693371814650284, STD: 0.19025980734977752


Degree-3 polynomial: R^2 for every fold: [0.30689692 0.1496736  0.38827092]
Degree-3 polynomial: Average R^2 for all the folds: 0.28161381160006743, STD: 0.23675178460286633


Degree-4 polynomial: R^2 for every fold: [0.7209975  0.40749117 0.84886534]
Degree-4 polynomial: Average R^2 for all the folds: 0.6591180032208857, STD: 0.18542670407038087

from sklearn.model_selection import cross_val_score
    from sklearn.model_selection import KFold
    from sklearn.metrics import r2_score
    
crossvalidation_poly = KFold(n_splits=3, shuffle=True) # Why are we using kfold=3 not 10; Because if you choose k=10, then you are increasing the points in validation set, so you are "using less data" to train the model

#for train_index, test_index in crossvalidation_poly.split(X_normalized):


for i in range(1,11):
    poly_cross_validation = PolynomialFeatures(degree=i)
    X_current = poly.fit_transform(X_normalized)
    model = lin_regressor.fit(X_current, y_for_normalized)
    scores = cross_val_score(model, X_current,y_for_normalized, scoring='r2', cv=crossvalidation_poly,
 n_jobs=1)
    

    print("\n\nDegree-"+str(i) +" polynomial: R^2 for every fold: " + str(np.abs(scores)))
          
          #+" training: " + str(np.abs(train_index))+" \ntesting: " + str(np.abs(test_index)))

    print('\033[1m'+"Degree-"+str(i)+ '\033[1m'+ " polynomial: Average R^2 for all the folds: " + str(np.mean(np.abs(scores))) + '\033[0m'+ ", STD: " + str(np.std(scores)))


Degree-1 polynomial: R^2 for every fold: [0.41300831 0.45801624 0.17011995]
Degree-1 polynomial: Average R^2 for all the folds: 0.34704816498535956, STD: 0.2860884371794798


Degree-2 polynomial: R^2 for every fold: [0.75123033 0.85035531 0.40642591]
Degree-2 polynomial: Average R^2 for all the folds: 0.6693371814650284, STD: 0.19025980734977752


Degree-3 polynomial: R^2 for every fold: [0.30689692 0.1496736  0.38827092]
Degree-3 polynomial: Average R^2 for all the folds: 0.28161381160006743, STD: 0.23675178460286633


Degree-4 polynomial: R^2 for every fold: [0.7209975  0.40749117 0.84886534]
Degree-4 polynomial: Average R^2 for all the folds: 0.6591180032208857, STD: 0.18542670407038087

from sklearn.model_selection import cross_val_score
    from sklearn.model_selection import KFold
    from sklearn.metrics import r2_score
    
crossvalidation_poly = KFold(n_splits=3, shuffle=True) 

#for train_index, test_index in crossvalidation_poly.split(X_normalized):


for i in range(1,11):
    poly_cross_validation = PolynomialFeatures(degree=i)
    X_current = poly.fit_transform(X_normalized)
    model = lin_regressor.fit(X_current, y_for_normalized)
    scores = cross_val_score(model, X_current,y_for_normalized, scoring='r2', cv=crossvalidation_poly,
 n_jobs=1)
    

    print("\n\nDegree-"+str(i) +" polynomial: R^2 for every fold: " + str(np.abs(scores)))
          
          #+" training: " + str(np.abs(train_index))+" \ntesting: " + str(np.abs(test_index)))

    print('\033[1m'+"Degree-"+str(i)+ '\033[1m'+ " polynomial: Average R^2 for all the folds: " + str(np.mean(np.abs(scores))) + '\033[0m'+ ", STD: " + str(np.std(scores)))


Degree-1 polynomial: R^2 for every fold: [0.41300831 0.45801624 0.17011995]
Degree-1 polynomial: Average R^2 for all the folds: 0.34704816498535956, STD: 0.2860884371794798


Degree-2 polynomial: R^2 for every fold: [0.75123033 0.85035531 0.40642591]
Degree-2 polynomial: Average R^2 for all the folds: 0.6693371814650284, STD: 0.19025980734977752


Degree-3 polynomial: R^2 for every fold: [0.30689692 0.1496736  0.38827092]
Degree-3 polynomial: Average R^2 for all the folds: 0.28161381160006743, STD: 0.23675178460286633


Degree-4 polynomial: R^2 for every fold: [0.7209975  0.40749117 0.84886534]
Degree-4 polynomial: Average R^2 for all the folds: 0.6591180032208857, STD: 0.18542670407038087

added 362 characters in body

Source Link

edited Aug 11, 2022 at 4:17

Z47

31
6

lin_regressor = LinearRegression()

# pass the order of your polynomial here  
poly = PolynomialFeatures(1)

# convert to be used further to linear regression
X_transform = poly.fit_transform(x_train)

# fit this to Linear Regressor
linear_regg=lin_regressor.fit(X_transform,y_train)

linear_regg.coef_

from sklearn.model_selection import cross_val_score
    from sklearn.model_selection import KFold
    from sklearn.metrics import r2_score
    
crossvalidation_poly = KFold(n_splits=3, shuffle=True) # Why are we using kfold=3 not 10; Because if you choose k=10, then you are increasing the points in validation set, so you are "using less data" to train the model

#for train_index, test_index in crossvalidation_poly.split(X_normalized):


for i in range(1,11):
    poly_cross_validation = PolynomialFeatures(degree=i)
    X_current = poly.fit_transform(X_normalized)
    model = lin_regressor.fit(X_current, y_for_normalized)
    scores = cross_val_score(model, X_current,y_for_normalized, scoring='r2', cv=crossvalidation_poly,
 n_jobs=1)
    

    print("\n\nDegree-"+str(i) +" polynomial: R^2 for every fold: " + str(np.abs(scores)))
          
          #+" training: " + str(np.abs(train_index))+" \ntesting: " + str(np.abs(test_index)))

    print('\033[1m'+"Degree-"+str(i)+ '\033[1m'+ " polynomial: Average R^2 for all the folds: " + str(np.mean(np.abs(scores))) + '\033[0m'+ ", STD: " + str(np.std(scores)))


Degree-1 polynomial: R^2 for every fold: [0.41300831 0.45801624 0.17011995]
Degree-1 polynomial: Average R^2 for all the folds: 0.34704816498535956, STD: 0.2860884371794798


Degree-2 polynomial: R^2 for every fold: [0.75123033 0.85035531 0.40642591]
Degree-2 polynomial: Average R^2 for all the folds: 0.6693371814650284, STD: 0.19025980734977752


Degree-3 polynomial: R^2 for every fold: [0.30689692 0.1496736  0.38827092]
Degree-3 polynomial: Average R^2 for all the folds: 0.28161381160006743, STD: 0.23675178460286633


Degree-4 polynomial: R^2 for every fold: [0.7209975  0.40749117 0.84886534]
Degree-4 polynomial: Average R^2 for all the folds: 0.6591180032208857, STD: 0.18542670407038087

from sklearn.model_selection import cross_val_score
    from sklearn.model_selection import KFold
    from sklearn.metrics import r2_score
    
crossvalidation_poly = KFold(n_splits=3, shuffle=True) # Why are we using kfold=3 not 10; Because if you choose k=10, then you are increasing the points in validation set, so you are "using less data" to train the model

#for train_index, test_index in crossvalidation_poly.split(X_normalized):


for i in range(1,11):
    poly_cross_validation = PolynomialFeatures(degree=i)
    X_current = poly.fit_transform(X_normalized)
    model = lin_regressor.fit(X_current, y_for_normalized)
    scores = cross_val_score(model, X_current,y_for_normalized, scoring='r2', cv=crossvalidation_poly,
 n_jobs=1)
    

    print("\n\nDegree-"+str(i) +" polynomial: R^2 for every fold: " + str(np.abs(scores)))
          
          #+" training: " + str(np.abs(train_index))+" \ntesting: " + str(np.abs(test_index)))

    print('\033[1m'+"Degree-"+str(i)+ '\033[1m'+ " polynomial: Average R^2 for all the folds: " + str(np.mean(np.abs(scores))) + '\033[0m'+ ", STD: " + str(np.std(scores)))


Degree-1 polynomial: R^2 for every fold: [0.41300831 0.45801624 0.17011995]
Degree-1 polynomial: Average R^2 for all the folds: 0.34704816498535956, STD: 0.2860884371794798


Degree-2 polynomial: R^2 for every fold: [0.75123033 0.85035531 0.40642591]
Degree-2 polynomial: Average R^2 for all the folds: 0.6693371814650284, STD: 0.19025980734977752


Degree-3 polynomial: R^2 for every fold: [0.30689692 0.1496736  0.38827092]
Degree-3 polynomial: Average R^2 for all the folds: 0.28161381160006743, STD: 0.23675178460286633


Degree-4 polynomial: R^2 for every fold: [0.7209975  0.40749117 0.84886534]
Degree-4 polynomial: Average R^2 for all the folds: 0.6591180032208857, STD: 0.18542670407038087

lin_regressor = LinearRegression()

# pass the order of your polynomial here  
poly = PolynomialFeatures(1)

# convert to be used further to linear regression
X_transform = poly.fit_transform(x_train)

# fit this to Linear Regressor
linear_regg=lin_regressor.fit(X_transform,y_train)

linear_regg.coef_

from sklearn.model_selection import cross_val_score
    from sklearn.model_selection import KFold
    from sklearn.metrics import r2_score
    
crossvalidation_poly = KFold(n_splits=3, shuffle=True) # Why are we using kfold=3 not 10; Because if you choose k=10, then you are increasing the points in validation set, so you are "using less data" to train the model

#for train_index, test_index in crossvalidation_poly.split(X_normalized):


for i in range(1,11):
    poly_cross_validation = PolynomialFeatures(degree=i)
    X_current = poly.fit_transform(X_normalized)
    model = lin_regressor.fit(X_current, y_for_normalized)
    scores = cross_val_score(model, X_current,y_for_normalized, scoring='r2', cv=crossvalidation_poly,
 n_jobs=1)
    

    print("\n\nDegree-"+str(i) +" polynomial: R^2 for every fold: " + str(np.abs(scores)))
          
          #+" training: " + str(np.abs(train_index))+" \ntesting: " + str(np.abs(test_index)))

    print('\033[1m'+"Degree-"+str(i)+ '\033[1m'+ " polynomial: Average R^2 for all the folds: " + str(np.mean(np.abs(scores))) + '\033[0m'+ ", STD: " + str(np.std(scores)))


Degree-1 polynomial: R^2 for every fold: [0.41300831 0.45801624 0.17011995]
Degree-1 polynomial: Average R^2 for all the folds: 0.34704816498535956, STD: 0.2860884371794798


Degree-2 polynomial: R^2 for every fold: [0.75123033 0.85035531 0.40642591]
Degree-2 polynomial: Average R^2 for all the folds: 0.6693371814650284, STD: 0.19025980734977752


Degree-3 polynomial: R^2 for every fold: [0.30689692 0.1496736  0.38827092]
Degree-3 polynomial: Average R^2 for all the folds: 0.28161381160006743, STD: 0.23675178460286633


Degree-4 polynomial: R^2 for every fold: [0.7209975  0.40749117 0.84886534]
Degree-4 polynomial: Average R^2 for all the folds: 0.6591180032208857, STD: 0.18542670407038087

added 59 characters in body

Source Link

edited Aug 11, 2022 at 2:56

Z47

31
6

Trying to do CV for my polynomial regressor. However, for some polynomial degrees:as the polynomial degree increases, R^2 decreases (e.g., R^2 for degree 2 is 0.6 while for degree 3 is 0.28), why is that?

from sklearn.model_selection import cross_val_score
    from sklearn.model_selection import KFold
    from sklearn.metrics import r2_score
    
crossvalidation_poly = KFold(n_splits=3, shuffle=True) # Why are we using kfold=3 not 10; Because if you choose k=10, then you are increasing the points in validation set, so you are "using less data" to train the model

#for train_index, test_index in crossvalidation_poly.split(X_normalized):


for i in range(1,11):
    poly_cross_validation = PolynomialFeatures(degree=i)
    X_current = poly.fit_transform(X_normalized)
    model = lin_regressor.fit(X_current, y_for_normalized)
    scores = cross_val_score(model, X_current,y_for_normalized, scoring='r2', cv=crossvalidation_poly,
 n_jobs=1)
    

    print("\n\nDegree-"+str(i) +" polynomial: R^2 for every fold: " + str(np.abs(scores)))
          
          #+" training: " + str(np.abs(train_index))+" \ntesting: " + str(np.abs(test_index)))

    print('\033[1m'+"Degree-"+str(i)+ '\033[1m'+ " polynomial: Average R^2 for all the folds: " + str(np.mean(np.abs(scores))) + '\033[0m'+ ", STD: " + str(np.std(scores)))


Degree-1 polynomial: R^2 for every fold: [0.41300831 0.45801624 0.17011995]
Degree-1 polynomial: Average R^2 for all the folds: 0.34704816498535956, STD: 0.2860884371794798


Degree-2 polynomial: R^2 for every fold: [0.75123033 0.85035531 0.40642591]
Degree-2 polynomial: Average R^2 for all the folds: 0.6693371814650284, STD: 0.19025980734977752


Degree-3 polynomial: R^2 for every fold: [0.30689692 0.1496736  0.38827092]
Degree-3 polynomial: Average R^2 for all the folds: 0.28161381160006743, STD: 0.23675178460286633


Degree-4 polynomial: R^2 for every fold: [0.7209975  0.40749117 0.84886534]
Degree-4 polynomial: Average R^2 for all the folds: 0.6591180032208857, STD: 0.18542670407038087

Trying to do CV for my polynomial regressor. However, for some polynomial degrees:as the polynomial degree increases, R^2 decreases, why is that?

from sklearn.model_selection import cross_val_score
    from sklearn.model_selection import KFold
    from sklearn.metrics import r2_score
    
crossvalidation_poly = KFold(n_splits=3, shuffle=True) # Why are we using kfold=3 not 10; Because if you choose k=10, then you are increasing the points in validation set, so you are "using less data" to train the model

#for train_index, test_index in crossvalidation_poly.split(X_normalized):


for i in range(1,11):
    poly_cross_validation = PolynomialFeatures(degree=i)
    X_current = poly.fit_transform(X_normalized)
    model = lin_regressor.fit(X_current, y_for_normalized)
    scores = cross_val_score(model, X_current,y_for_normalized, scoring='r2', cv=crossvalidation_poly,
 n_jobs=1)
    

    print("\n\nDegree-"+str(i) +" polynomial: R^2 for every fold: " + str(np.abs(scores)))
          
          #+" training: " + str(np.abs(train_index))+" \ntesting: " + str(np.abs(test_index)))

    print('\033[1m'+"Degree-"+str(i)+ '\033[1m'+ " polynomial: Average R^2 for all the folds: " + str(np.mean(np.abs(scores))) + '\033[0m'+ ", STD: " + str(np.std(scores)))


Degree-1 polynomial: R^2 for every fold: [0.41300831 0.45801624 0.17011995]
Degree-1 polynomial: Average R^2 for all the folds: 0.34704816498535956, STD: 0.2860884371794798


Degree-2 polynomial: R^2 for every fold: [0.75123033 0.85035531 0.40642591]
Degree-2 polynomial: Average R^2 for all the folds: 0.6693371814650284, STD: 0.19025980734977752


Degree-3 polynomial: R^2 for every fold: [0.30689692 0.1496736  0.38827092]
Degree-3 polynomial: Average R^2 for all the folds: 0.28161381160006743, STD: 0.23675178460286633


Degree-4 polynomial: R^2 for every fold: [0.7209975  0.40749117 0.84886534]
Degree-4 polynomial: Average R^2 for all the folds: 0.6591180032208857, STD: 0.18542670407038087

Trying to do CV for my polynomial regressor. However, for some polynomial degrees:as the polynomial degree increases, R^2 decreases (e.g., R^2 for degree 2 is 0.6 while for degree 3 is 0.28), why is that?

from sklearn.model_selection import cross_val_score
    from sklearn.model_selection import KFold
    from sklearn.metrics import r2_score
    
crossvalidation_poly = KFold(n_splits=3, shuffle=True) # Why are we using kfold=3 not 10; Because if you choose k=10, then you are increasing the points in validation set, so you are "using less data" to train the model

#for train_index, test_index in crossvalidation_poly.split(X_normalized):


for i in range(1,11):
    poly_cross_validation = PolynomialFeatures(degree=i)
    X_current = poly.fit_transform(X_normalized)
    model = lin_regressor.fit(X_current, y_for_normalized)
    scores = cross_val_score(model, X_current,y_for_normalized, scoring='r2', cv=crossvalidation_poly,
 n_jobs=1)
    

    print("\n\nDegree-"+str(i) +" polynomial: R^2 for every fold: " + str(np.abs(scores)))
          
          #+" training: " + str(np.abs(train_index))+" \ntesting: " + str(np.abs(test_index)))

    print('\033[1m'+"Degree-"+str(i)+ '\033[1m'+ " polynomial: Average R^2 for all the folds: " + str(np.mean(np.abs(scores))) + '\033[0m'+ ", STD: " + str(np.std(scores)))


Degree-1 polynomial: R^2 for every fold: [0.41300831 0.45801624 0.17011995]
Degree-1 polynomial: Average R^2 for all the folds: 0.34704816498535956, STD: 0.2860884371794798


Degree-2 polynomial: R^2 for every fold: [0.75123033 0.85035531 0.40642591]
Degree-2 polynomial: Average R^2 for all the folds: 0.6693371814650284, STD: 0.19025980734977752


Degree-3 polynomial: R^2 for every fold: [0.30689692 0.1496736  0.38827092]
Degree-3 polynomial: Average R^2 for all the folds: 0.28161381160006743, STD: 0.23675178460286633


Degree-4 polynomial: R^2 for every fold: [0.7209975  0.40749117 0.84886534]
Degree-4 polynomial: Average R^2 for all the folds: 0.6591180032208857, STD: 0.18542670407038087

Source Link

asked Aug 11, 2022 at 2:55

Z47

31
6

Loading

Stack Exchange Network

Return to Question