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I am using the Ridge linear regression from sickit learn. In the documentation they stated that the alpha parameter has to be small.

However I am getting my best model performance at 6060. Am I doing something wrong ?

Here is the description from documentation:

alpha : {float, array-like} shape = [n_targets] Small positive values
of alpha improve the conditioning of the problem and reduce the
variance of the estimates.

Here is my code:

import pandas as pd
import numpy as np
import custom_metrics as cmetric
from sklearn import preprocessing
from sklearn import cross_validation
from sklearn import linear_model

# Read data files:
df_train = pd.read_csv(path + "/input/train.csv")
df_test  = pd.read_csv(path + "/input/test.csv")

#print df.shape
#(50999, 34)

#convert categorical features into integers
feature_cols_obj = [col for col in df_train.columns if df_train[col].dtypes == 'object']
le = preprocessing.LabelEncoder()
for col in feature_cols_obj:
    df_train[col] = le.fit_transform(df_train[col])
    df_test[col] = le.transform(df_test[col])

#Scale the data so that each feature has zero mean and unit std
feature_cols = [col for col in df_train.columns if col not in ['Hazard','Id']]
scaler = preprocessing.StandardScaler().fit(df_train[feature_cols])
df_train[feature_cols] = scaler.transform(df_train[feature_cols])                               
df_test[feature_cols] = scaler.transform(df_test[feature_cols]) 

#polynomial features/interactions
X_train = df_train[feature_cols]
X_test = df_test[feature_cols]
y = df_train['Hazard']
test_ids = df_test['Id']
poly = preprocessing.PolynomialFeatures(2)
X_train = poly.fit_transform(X_train)
X_test = poly.fit_transform(X_test)

#do grid search to find best value for alpha
#alphas = np.arange(-10,3,1)        
#clf = linear_model.RidgeCV(10**alphas)
alphas = np.arange(100,10000,10)        
clf = linear_model.RidgeCV(alphas)
clf.fit(X_train, y)
print clf.alpha_  
#clf.alpha=6060

cv = cross_validation.KFold(df_train.shape[0], n_folds=10)
mse = []
mse_train = []
fold_count = 0
for train, test in cv:
    print("Processing fold %s" % fold_count)
    train_fold = df_train.ix[train]
    test_fold = df_train.ix[test]

    # Get training examples
    X_train = train_fold[feature_cols]
    y = train_fold['Hazard']
    X_test = test_fold[feature_cols]
    #interactions
    poly = preprocessing.PolynomialFeatures(2)
    X_train = poly.fit_transform(X_train)
    X_test = poly.fit_transform(X_test)

    # Fit Ridge linear regression 
    cfr = linear_model.Ridge (alpha = 6060)
    cfr.fit(X_train, y)

    # Check error on test set
    pred = cfr.predict(X_test)

    mse.append(cmetric.normalized_gini(test_fold.Hazard, pred))

    # Check error on training set (Resubsitution error)
    mse_train.append(cmetric.normalized_gini(y, cfr.predict(X_train)))    

    # Done with the fold
    fold_count += 1

    #print model coeff

print cfr.coef_

print pd.DataFrame(mse).mean()
#0.311794
print pd.DataFrame(mse_train).mean()
#.344775

This is the parameters of my model

[  0.00000000e+00   5.01056266e-02   3.38358145e-01   1.30415614e-01
   1.96089173e-01   1.25423106e-01  -1.72319456e-02   1.02133523e-01
   2.81574892e-01   8.95633136e-02  -5.88384438e-03   1.47409573e-01
   1.33623390e-01  -1.23180872e-02  -1.46668969e-01  -4.92436419e-02
   1.99181255e-01  -4.04964277e-03  -1.53413757e-01  -1.44825780e-01
  -3.91212516e-03   3.31216145e-03  -6.26732347e-02   2.88351008e-02
  -2.06225972e-03  -5.62389494e-02  -1.36303417e-01  -9.71481638e-03
  -2.50177992e-02  -5.66878847e-03   5.27927411e-03   8.52720405e-02
   2.06771941e-01   1.56008577e-01   6.40581708e-04   9.92281016e-03
  -9.19795609e-02   3.12156134e-02   5.99317391e-03   2.97288547e-02
   8.18623392e-02   2.29032549e-02  -2.73972788e-02   1.51645073e-02
   3.23438207e-02   3.88545534e-02   2.09627935e-02   6.96394351e-02
  -9.16980407e-03  -2.18354808e-02   5.07216880e-03   3.17494225e-02
  -2.09772938e-02   7.49790681e-02   1.64625955e-02   1.62684403e-02
   1.75895590e-02  -1.75381993e-02   3.30949594e-02   1.68392658e-02
  -4.66582083e-02  -1.31719587e-02   2.87477287e-02   3.09746600e-02
   4.02686924e-02   9.92987348e-02   6.68115596e-02   1.37739367e-02
   2.59549211e-02  -2.38058399e-02   2.65402587e-02  -6.92529979e-04
   1.29576451e-02   1.25610137e-02  -9.68450401e-03  -2.27944079e-03
   8.09259777e-03   3.30342301e-02  -1.66721756e-02   2.23839435e-02
   3.32432426e-02  -8.04561602e-04  -1.76497454e-01   3.88186056e-02
   3.37774181e-02   2.17565099e-02   5.30233710e-03  -9.24771708e-03
  -2.73679575e-02   1.85809743e-02   1.29401582e-02  -3.19690493e-02
   6.66584177e-03   4.49614784e-02   1.54566766e-02  -7.53477425e-02
   5.81757746e-02  -1.76431610e-02   2.75413678e-02  -2.55708758e-02
  -1.45602981e-02   1.81886720e-02  -2.32100056e-02  -3.80762864e-02
   1.23351328e-02  -1.66785206e-02   1.56719872e-02   4.68276318e-03
   9.40509132e-04   3.57552385e-02  -1.58076069e-02  -5.53826979e-02
  -6.65141956e-03  -2.88814865e-03   1.50011930e-02   2.13362782e-02
  -2.81424369e-03  -2.31808199e-02  -7.58749682e-04  -2.14478348e-02
  -2.51214499e-02  -1.79191990e-02  -4.81870440e-03  -1.46611980e-02
  -4.94190983e-03   3.70234969e-02  -1.02883622e-01   2.76857570e-02
   1.79941196e-02   1.32435722e-02   4.76814155e-02   3.65520203e-02
  -3.40269596e-02   2.28209650e-02   2.64274614e-02  -1.27865165e-02
  -2.27199591e-02   8.70615230e-02   6.13932119e-02  -1.08140405e-02
  -4.25732617e-02   2.77774841e-02   2.61014304e-02  -2.11770868e-02
  -3.23724937e-02  -1.89128329e-02  -1.05251080e-02   1.83862325e-02
   2.23534204e-05  -1.20347566e-02  -9.01096911e-03   4.02046530e-02
   1.98012305e-02   1.58194352e-02   1.12816659e-02   2.20555788e-02
   3.63227509e-03   8.58770347e-03   1.02248600e-02   9.08000210e-03
  -3.46537486e-03   3.12890495e-02  -1.43673284e-02   3.14534787e-02
  -2.75188217e-02  -7.18691836e-03  -7.07891187e-03   2.31015874e-03
   1.35687890e-03   1.19905667e-02   1.67455167e-02  -4.81069735e-02
  -9.68752624e-03   1.07210195e-02   2.21967422e-02  -1.01291741e-02
   5.25316073e-02  -6.66390427e-03   1.14009388e-02  -2.01902980e-02
   7.12558770e-02   7.83356049e-03   2.38237767e-02  -4.15273084e-03
   8.77559520e-03  -9.00060067e-03   1.60980039e-02  -1.08296154e-02
  -4.42603447e-02  -1.09092326e-02  -1.44739014e-02  -8.60951329e-03
   2.49086682e-02  -1.92284756e-02  -1.89749837e-02  -2.77355424e-02
   9.82524416e-04   5.67031203e-03  -2.54535190e-03   4.75299754e-03
   2.71211354e-02   3.27688397e-03   1.85424999e-02  -2.26283972e-03
  -1.79189346e-02   1.71016295e-02   1.93496703e-02  -8.69306494e-03
  -9.58453162e-03   1.20178271e-02  -2.26289764e-02   2.15726732e-03
   8.10821412e-03   2.47074350e-02   2.95059846e-02   1.21555107e-03
   4.98131914e-03   2.43000118e-03   1.95785508e-02  -1.57990583e-02
  -1.16102797e-02   7.46115157e-03  -8.06557912e-03   2.15298282e-02
   2.29129769e-03   3.25367516e-02   1.99525909e-02  -3.92835829e-05
  -2.05836804e-02   5.04866199e-03   1.24307792e-02   2.53079097e-02
   1.96925968e-02  -2.64611443e-02  -6.82689419e-03  -1.49852524e-02
  -3.93645529e-02   9.99089648e-03   1.09631668e-02  -1.51040704e-02
   1.67164079e-02   1.26766125e-02  -5.86334604e-02   2.40496926e-02
   1.54186622e-02  -6.12083319e-02   2.96323772e-02  -2.44415176e-02
   1.11052819e-02  -2.57457149e-02  -2.49398749e-02   3.32951848e-02
   3.85385282e-02  -5.16258286e-02   9.54478785e-03  -1.72063013e-02
   2.23740124e-02  -5.52438260e-03  -1.31083373e-02   4.06350280e-02
   2.55388980e-02  -1.41308581e-02  -5.75406964e-03  -2.16662792e-02
   1.62563844e-02  -2.24345285e-02  -3.11828721e-02   1.44461933e-02
  -1.30242777e-02   5.54219131e-03   7.95690283e-03   1.76646739e-03
   1.41692278e-02   1.86635350e-02  -1.97979179e-02  -4.63186884e-03
   1.20542175e-02   3.20413779e-02  -4.57051394e-02  -2.36441701e-02
  -3.04932172e-02   3.87911664e-02   4.78728082e-02  -1.88170992e-02
   2.63657803e-03  -3.86012566e-03   3.97224532e-03   1.39442494e-02
  -1.88336565e-02  -2.70551779e-02  -4.66568493e-03  -1.33610215e-03
  -8.18744988e-03   8.46266586e-03   1.48045340e-02  -6.83182810e-03
   4.27071232e-04  -2.06468268e-03  -4.97468097e-03   1.48996773e-02
   1.07555873e-03  -9.22835391e-03   8.99547441e-03   4.82968523e-03
   9.98661438e-03  -1.65016157e-02   4.92553539e-03  -1.16019345e-03
  -8.61715302e-02   3.61199006e-02  -3.42490963e-02   1.90392013e-03
  -2.28637135e-02  -5.21567166e-02   2.52407362e-02  -4.18485080e-02
  -1.10058841e-02   1.08156107e-02   2.75855699e-02   3.42679472e-02
  -2.20825398e-02   3.10296716e-02  -2.75477891e-02  -3.07610994e-04
  -9.01535833e-03   1.83193047e-02  -1.62208155e-02  -3.10351309e-02
   2.48818137e-02   8.18365382e-03  -1.60809925e-02   1.01836062e-02
  -2.05476464e-02   6.85855700e-03   2.57900195e-02  -1.49888744e-02
  -1.74511929e-03   1.24756224e-02   6.52823373e-03  -8.66673208e-03
   4.31158765e-02  -3.38250310e-02   3.18997087e-02  -1.37758806e-02
  -5.33139333e-03  -8.79443447e-03  -1.44610591e-02   2.52537246e-02
   7.87391233e-02   1.27012172e-02  -1.56102214e-02  -2.67977090e-02
  -4.62736835e-04   2.56238335e-02  -8.09176226e-03   1.91149252e-03
   2.22919180e-03  -1.68315172e-02   7.52355012e-04   8.54417905e-03
   4.70626447e-03   3.26721691e-02  -6.66386713e-03  -3.62252305e-02
  -1.58279947e-03   9.68094966e-04  -1.48804245e-02   7.77251715e-03
   3.10671736e-02  -2.88045626e-02  -4.11328551e-03  -8.85415876e-03
   1.00068277e-02  -1.91264954e-02   2.67619648e-03   4.45828413e-02
   3.10793047e-02  -5.73633264e-03  -1.42399778e-02  -1.64262324e-02
   3.46889578e-03  -2.07657571e-02   4.23753762e-02  -1.34629372e-04
   1.29942385e-02   2.76672570e-02   2.42359462e-02  -3.10531938e-02
  -6.55599208e-03  -2.99614420e-02  -1.91772543e-03  -2.02543378e-02
   2.21573145e-02  -1.59205200e-02  -4.01668972e-02   1.68476566e-02
   2.37997259e-02   9.68827220e-03   2.31875156e-02   6.79334701e-03
   8.50905759e-03   2.75432711e-02  -1.15121814e-02  -3.73346961e-02
  -1.38350227e-02   1.80944227e-03  -1.99144252e-02  -4.50820362e-02
  -8.51953547e-02   1.05289990e-03  -5.73683988e-02  -2.28014261e-03
   8.79845471e-04  -1.78715467e-02   3.80136044e-02   5.91779029e-03
  -2.78439138e-02   1.17008295e-02  -3.42645883e-02   2.34195563e-02
  -4.81212125e-03  -3.66954676e-03   3.90228979e-02  -1.70824631e-02
   1.26012065e-02  -6.31776451e-03  -4.50539802e-02   4.56076309e-03
   1.44345103e-04   7.18085486e-03  -5.65887042e-03  -8.93522131e-03
   1.10250325e-02  -7.96661764e-03   3.41027635e-03   1.22731705e-02
   8.47707142e-03  -1.49932019e-02   2.66278446e-02  -1.91671698e-02
  -1.26043505e-02   6.35412651e-02  -1.96684538e-02   1.54777089e-02
   1.91255149e-02   5.31808863e-02   5.35289710e-04  -2.08611895e-03
  -4.96139883e-05   3.58330048e-02  -4.11211604e-03  -2.71141250e-02
  -3.69387375e-02   1.32678215e-02   1.03065894e-02  -1.16026233e-01
   9.05902436e-03  -4.11355240e-03  -5.76609367e-03  -3.03489660e-02
  -2.28466980e-02  -4.07422105e-03  -1.14981380e-02  -2.00718306e-02
   2.82733363e-02  -5.85023917e-03   3.73266757e-02  -6.81585169e-02
  -5.58717156e-02  -3.08019223e-02  -2.96969413e-03  -2.47161214e-02
  -4.22694385e-03  -7.48483026e-03  -5.56253994e-03   7.40543585e-04
   3.01216667e-02  -5.56430481e-03   5.64963486e-03  -3.23841390e-02
   8.53283403e-03   1.11517051e-02   9.92444066e-03  -1.23128623e-01
   9.55844602e-03  -1.99321384e-02   1.57922080e-02   1.19673131e-02
   1.68849528e-02  -6.34044465e-03   1.06775644e-02   2.47265340e-02
  -3.25711720e-02  -9.76594327e-03  -5.08742553e-02   5.24289526e-02
   2.91111239e-02  -1.39398617e-02   2.42465106e-02  -4.15577108e-02
  -2.58480889e-02   4.62777932e-02   1.20306488e-02   2.75909133e-03
  -1.01712845e-02  -5.46886148e-02  -2.46527009e-02  -1.01558015e-02
   1.56187669e-02   3.52148277e-03   2.19565752e-02  -8.63359919e-03
  -1.76395758e-02   1.96950103e-02   1.48984342e-02  -3.16258423e-03
  -5.85331096e-03   9.65977546e-03   4.50183244e-03  -2.47884005e-03
  -1.69232421e-02  -5.99840290e-04   6.71455978e-04   1.08295297e-02
   1.95363677e-02   9.41925140e-03  -1.81041432e-02  -1.40310535e-02
   7.22752555e-04   2.96587727e-02  -3.23319552e-02  -3.06897437e-02
  -1.84134215e-02   6.59667420e-02   2.65303333e-02   3.17956491e-02
   1.27969978e-02  -2.03537673e-02  -2.66071290e-02  -7.43361712e-03
  -2.48459980e-02   3.64371936e-03   1.64657605e-02  -4.65377776e-02
  -8.32882233e-03   2.52378813e-02   2.51187743e-02  -1.62291204e-02
  -1.84450879e-02   3.42146322e-02  -3.21809348e-02  -9.33033795e-03
  -9.45292979e-03  -3.45051567e-02  -3.55155679e-02  -1.25766013e-01
  -2.02891251e-02   5.37952007e-03   1.27094363e-02   2.36198128e-02
   2.32853839e-02]
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7
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The L2 norm term in ridge regression is weighted by the regularization parameter alpha

So, if the alpha value is 0, it means that it is just an Ordinary Least Squares Regression model. So, the larger is the alpha, the higher is the smoothness constraint.

So, the smaller the value of alpha, the higher would be the magnitude of the coefficients.

I would add an image which would help you visualize how the alpha value influences the fit:

enter image description here

So, the alpha parameter need not be small. But, for a larger alpha, the flexibility of the fit would be very strict.

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  • $\begingroup$ Could be that the model doesn't fit very well. With a very large alpha, the algorithm more or else ignores the IV's and fits a mean. $\endgroup$ – Placidia Aug 13 '15 at 11:16
  • $\begingroup$ @Placidia, yes I would completely agree with your comment. I was just trying to explain the significance of alpha as a parameter (as asked in the question) in Ridge Regression, and how it's change would affect the fit and the coefficients. Thank you for including the point in the comment. $\endgroup$ – Dawny33 Aug 13 '15 at 11:24

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