Prob 4-1 with Sklearn¶
For every order, you have to do the cross-validation to choose the best model. You need to record the validation error (27 values) and assign on your report. Use the best model to test the training set (10 point) and the test set, you would get training error and the test error for the order. Draw the figure (error vs order) with the training and test error.
In [1]:
%matplotlib inline
import numpy as np
import pandas as pd
import matplotlib
import matplotlib .pyplot as plt
from sklearn.model_selection import KFold
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import make_pipeline
from sklearn import linear_model
In [2]:
data4 = pd.read_csv("x3t3.csv")
將training set切割成三個子集, 輪流當validation set¶
valid_x1 = np.array(data4.train_x[0:5]).reshape(-1,1)
valid_y1 = np.array(data4.train_y[0:5])
valid_x2 = np.array(data4.train_x[5:10]).reshape(-1,1)
valid_y2 = np.array(data4.train_y[5:10])
valid_x3 = np.array(data4.train_x[10:15]).reshape(-1,1)
valid_y3 = np.array(data4.train_y[10:15])
train_x1 = np.array(data4.train_x[5:15]).reshape(-1,1)
train_y1 = np.array(data4.train_y[5:15])
train_x2 = np.append(valid_x1,valid_x3).reshape(-1,1)
train_y2 = np.append(valid_y1,valid_y3)
train_x3 = np.array(data4.train_x[0:10]).reshape(-1,1)
train_y3 = np.array(data4.train_y[0:10])
train_x123 = [train_x1,train_x2,train_x3] train_y123 = [train_y1,train_y2,train_y3] valid_x123 = [valid_x1,valid_x2,valid_x3] valid_y123 = [valid_y1,valid_y2,valid_y3] test_x = np.array(data4.test_x[0:10]).reshape(-1,1) test_y = np.array(data4.test_y[0:10])
print valid_x1 print valid_x3 print train_x2
print valid_y1 print valid_y3 print train_y2
Validation¶
In [ ]:
def Reg_CV(degree): #cross_validation, 挑某一個當作validation set, 而其他的用來training
#---將training set切割成三個子集, 輪流當validation set---
kf = KFold(n_splits=3)
V_Err = []
for train, test in kf.split(range(15)):
train_x = np.array(data4.train_x[train]).reshape(-1,1)
train_y = np.array(data4.train_y[train])
test_x = np.array(data4.train_x[test]).reshape(-1,1)
test_y = np.array(data4.train_y[test])
#---------build up model---------------------------
reg = linear_model.LinearRegression()
est = make_pipeline(PolynomialFeatures(degree), reg)
est.fit(train_x, train_y)
#---------predict y---------------------------
pred_y = est.predict(test_x)
#n = pred_y.size
#return np.sqrt( np.sum( ( test_y - pred_y )**2 ) /n )
VE = 0.5* np.sum( np.square( test_y - pred_y ) ) #validation error
V_Err.append(VE)
return V_Err
Reg_CV(2)
In [ ]:
D = [] #order/degree
E = [] #Valid_Error
for deg in range(1,10):
D.append(deg)
E.append ( np.log(Reg_CV(deg)) )
Err = pd.DataFrame(np.matrix(E),index=['deg_'+str(i) for i in range(1,10)],
columns=['valid_set'+str(i) for i in range(1,4)],dtype=float)
Err['AVG_Valid_Err'] = [ Err.iloc[i,:].sum()/3 for i in range(0,9)] #計算平均valid_err for each degree
Err.to_csv('Prob4_valid_err.csv')
In [ ]:
plt.plot(D, Err['valid_set1'], 'r--', D, Err['valid_set2'], 'g--',
D, Err['valid_set3'], 'y--', D, Err['AVG_Valid_Err'], 'b-',linewidth=2)
plt.title('order vs. valid_err, red:valid_set1, green:valid_set2, yellow:valid_set3, blue:avg ')
plt.xlabel('order M')
plt.ylabel('log(valid_err)')
plt
Testing¶
In [49]:
def Reg(train_x, train_y,test_x,test_y,degree): #train -> test
#---------build up model---------------------------
reg = linear_model.LinearRegression()
est = make_pipeline(PolynomialFeatures(degree), reg)
est.fit(train_x, train_y)
#---------predict y---------------------------
pred_y = est.predict(test_x)
#n = pred_y.size
#return np.sqrt( np.sum( ( test_y - pred_y )**2 ) /n )
E = 0.5* np.sum( np.square( test_y - pred_y ) )
#---------plot---------------------------
linX = np.linspace(0,6,1000).reshape(-1,1)
plt.plot(test_x,test_y,'ro', linX, est.predict(linX), 'b-')
plt.title('Degree='+str(degree))
plt.xlabel('X')
plt.ylabel('Y')
#plt.show()
plt.savefig('prob4_fig/deg'+str(degree)+'.jpg')
plt.close()
return E
D = [] #order/degree
T_E = [[],[],[]] #Error function for Testing set
for deg in range(1,10):
D.append(deg)
for i in range(3):
train_x = np.array(data4.train_x[i5:i5+5]).reshape(-1,1)
train_y = np.array(data4.train_y[i5:i5+5])
T_E[i].append (Reg(train_x,train_y,deg)) #算出來近似
print T_E
Err = pd.DataFrame(np.matrix(TE).transpose(),index=['deg'+str(i) for i in range(1,10)], columns=['valid_set'+str(i) for i in range(1,4)])
Err['AVG_test_Err'] = [ Err.iloc[i,:].sum()/3 for i in range(0,9)] #計算平均valid_err for each degree Err.to_csv('Prob4_test_err.csv')
plt.plot(D, np.log(T_E[0]), 'r--', D, np.log(T_E[1]), 'g--', D, np.log(T_E[2]), 'y--', D, np.log(Err['AVG_test_Err']), 'b-',linewidth=2) plt.title('order vs. Error, red:valid_set1, green:valid_set2, yellow:valid_set3, blue:avg ') plt.xlabel('order M') plt.ylabel('log(Error)')
In [50]:
train_x_all = np.array(data4.train_x).reshape(-1,1)
train_y_all = np.array(data4.train_y)
test_x_all = np.array(data4.test_x[0:10]).reshape(-1,1)
test_y_all = np.array(data4.test_y[0:10])
In [54]:
D = [] #order/degree
T_E = [[],[]] #Error function for Training/Testing set
max_deg = 12
for deg in range(1,max_deg+1,1):
D.append(deg)
T_E[0].append (Reg(train_x_all,train_y_all,train_x_all,train_y_all,deg))
T_E[1].append (Reg(train_x_all,train_y_all,test_x_all,test_y_all,deg))
#print T_E
T_E.append(D)
Err = pd.DataFrame(np.matrix(T_E).transpose(),index=D,
columns=['Training set','Testing set','degree'])
Err['AVG_test_Err'] = (Err['Training set']+Err['Testing set'])/2 #計算平均test_err for each degree
Err.to_csv('Prob4_test_err.csv')
Err
Out[54]:
| Training set | Testing set | degree | AVG_test_Err | |
|---|---|---|---|---|
| 1 | 8.571835 | 26.843082 | 1.0 | 17.707458 |
| 2 | 8.286504 | 25.546623 | 2.0 | 16.916563 |
| 3 | 4.536034 | 14.229472 | 3.0 | 9.382753 |
| 4 | 3.142099 | 12.037603 | 4.0 | 7.589851 |
| 5 | 2.350315 | 10.938616 | 5.0 | 6.644466 |
| 6 | 2.320304 | 9.968271 | 6.0 | 6.144288 |
| 7 | 2.318721 | 9.564454 | 7.0 | 5.941588 |
| 8 | 2.237168 | 12.549179 | 8.0 | 7.393173 |
| 9 | 2.124401 | 13.195951 | 9.0 | 7.660176 |
| 10 | 1.806509 | 6.998457 | 10.0 | 4.402483 |
| 11 | 1.195913 | 349.932292 | 11.0 | 175.564102 |
| 12 | 1.065494 | 2379.776527 | 12.0 | 1190.421011 |
In [55]:
plt.plot( D, np.log(Err['Training set']), 'b-',D, np.log(Err['Testing set']), 'r-',linewidth=2)
plt.title('order vs. Error, blue:Train, red:Test')
plt.xlabel('order M')
plt.ylabel('log(Error)')
Out[55]:
<matplotlib.text.Text at 0x12627400>
Prob 4-2 with Sklearn¶
In [70]:
def Reg_L2(train_x, train_y,test_x, test_y,degree,lenda,if_plot_coeff):
#---------build up model---------------------------
reg = linear_model.Ridge(alpha=lenda,fit_intercept=False)
est = make_pipeline(PolynomialFeatures(degree), reg)
est.fit(train_x, train_y)
#---------find coeff---------------------------
#print est.steps
coef = est.steps[-1][1].coef_#.ravel()
coef_pair = zip(np.abs(coef),range(coef.size))
feature_names = est.steps[0][1].get_feature_names()
print 'feature_names=',feature_names
print 'coef=',coef
#---------plot coeff---------------------------
if if_plot_coeff:
print 'plot:'
plt.plot(range(coef.size),np.abs(coef),'b-')
plt.xlabel('coef order')
plt.ylabel('abs(w)')
plt.title('Coef Weight, deg='+str(degree)+',lambda='+str(lenda))
#plt.show()
plt.savefig('prob4_fig\CoefWeight_deg'+str(degree)+'_lambda'+str(lenda)+'.jpg')
plt.close()
#---------predict y---------------------------
pred_y = est.predict(test_x)
#n = pred_y.size
#return np.sqrt( np.sum( ( test_y - pred_y )**2 ) /n )
return 0.5* np.sum( np.square( test_y - pred_y ) ) + 0.5 * lenda * np.sum( np.square( coef ) )
In [76]:
train_x = np.array(data4.train_x).reshape(-1,1)
train_y = np.array(data4.train_y)
test_x = np.array(data4.test_x[0:10]).reshape(-1,1)
test_y = np.array(data4.test_y[0:10])
train_x.size
Out[76]:
15
In [77]:
%matplotlib inline
degree = 9
L = [] #lenda
E_T = [] #Error for sum
min_e = [0,350000] # i,j,e_t,e_d,e_w
for j in range(0,100,10): #設定lenda範圍
l = (float)(j)/100
print 'Lambda =', l
print ''
e = Reg_L2(train_x, train_y,test_x, test_y, degree, l, True)
L.append( l )
E_T.append( e )
print 'Err =', [l,e]
if min_e[1] > e :
min_e = [l,e]
print ''
print "*" *64
print ''
print "min_e = " , min_e # 算出[0.3, 8.7275293447745863] 與原本答案[0.3, 8.7275410196083474]很接近
Lambda = 0.0 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ 4.29451379e-01 -6.91572638e+00 -4.05566049e+00 3.39835369e+01 -3.96137666e+01 2.15095027e+01 -6.43998997e+00 1.09257646e+00 -9.84629104e-02 3.66330473e-03] plot: Err = [0.0, 13.1954895893375] **************************************************************** Lambda = 0.1 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -3.24889591e-02 -6.90598379e-01 -1.84824226e-01 1.82289107e-01 2.39800301e-01 4.16016944e-02 -1.41922222e-01 5.21695197e-02 -7.37506470e-03 3.71054331e-04] plot: Err = [0.1, 8.7524238591132555] **************************************************************** Lambda = 0.2 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.53770693e-02 -5.26787416e-01 -1.88926386e-01 1.06154451e-01 2.21756758e-01 9.12063473e-02 -1.64549184e-01 5.68590399e-02 -7.84679868e-03 3.89763703e-04] plot: Err = [0.2, 8.7287894882406736] **************************************************************** Lambda = 0.3 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.38400856e-02 -4.41112865e-01 -1.78501296e-01 7.42943248e-02 2.05665668e-01 1.10302886e-01 -1.70120976e-01 5.74717358e-02 -7.85749937e-03 3.88255280e-04] plot: Err = [0.3, 8.7275293447745863] **************************************************************** Lambda = 0.4 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.57526925e-02 -3.85467117e-01 -1.66442794e-01 5.80881413e-02 1.93147277e-01 1.17672571e-01 -1.69849817e-01 5.67750905e-02 -7.72676266e-03 3.80759163e-04] plot: Err = [0.4, 8.7321895488409957] **************************************************************** Lambda = 0.5 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [-0.10389032 -0.34521552 -0.15491962 0.04896698 0.18311756 0.11987705 -0.16730769 0.05561591 -0.00755001 0.00037145] plot: Err = [0.5, 8.7384436033990074] **************************************************************** Lambda = 0.6 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [-0.10958073 -0.31417003 -0.14438783 0.04352198 0.17482886 0.11959357 -0.16386837 0.05430904 -0.00736188 0.00036182] plot: Err = [0.6, 8.7448578250588991] **************************************************************** Lambda = 0.7 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [-0.11357416 -0.28919014 -0.1348822 0.0401603 0.16781076 0.11805615 -0.16012415 0.0529842 -0.00717615 0.00035245] plot: Err = [0.7, 8.7509278368218482] **************************************************************** Lambda = 0.8 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [-0.11633965 -0.26848014 -0.12632214 0.03805294 0.16175562 0.11588578 -0.15634829 0.05169727 -0.00699841 0.00034355] plot: Err = [0.8, 8.7564915311691713] **************************************************************** Lambda = 0.9 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [-0.11819073 -0.25092342 -0.11860055 0.03673514 0.15645333 0.1134122 -0.15266882 0.05047138 -0.00683067 0.0003352 ] plot: Err = [0.9, 8.7615235936507805] **************************************************************** min_e = [0.3, 8.7275293447745863]
In [83]:
plt.plot(L, np.log(E_T) , 'b-')
plt.title('$Lambda \ vs. Error, blue:E(w)=E_D+E_W$')
plt.xlabel('lambda')
plt.ylabel('log( E(w) )')
Out[83]:
<matplotlib.text.Text at 0x1234bc18>
In [85]:
Err = pd.DataFrame({'lambda':L,
'log(E)':np.log(E_T)})
Err
Out[85]:
| lambda | log(E) | |
|---|---|---|
| 0 | 0.0 | 2.579875 |
| 1 | 0.1 | 2.169331 |
| 2 | 0.2 | 2.166627 |
| 3 | 0.3 | 2.166482 |
| 4 | 0.4 | 2.167016 |
| 5 | 0.5 | 2.167732 |
| 6 | 0.6 | 2.168466 |
| 7 | 0.7 | 2.169160 |
| 8 | 0.8 | 2.169795 |
| 9 | 0.9 | 2.170370 |
In [86]:
%matplotlib inline
degree = 9
L = [] #lenda
E_T = [] #Error for sum
min_e = [0,350000] # i,j,e_t,e_d,e_w
for j in range(200,400): #設定lenda範圍
l = (float)(j)/1000
print 'Lambda =', l
print ''
e = Reg_L2(train_x, train_y,test_x, test_y, degree, l, False)
L.append( l )
E_T.append( e )
print 'Err =', [l,e]
if min_e[1] > e :
min_e = [l,e]
print ''
print "*" *64
print ''
print "min_e = " , min_e # 算出[0.3, 8.7275293447745863] 與原本答案[0.3, 8.7275410196083474]很接近
Lambda = 0.2 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.53770693e-02 -5.26787416e-01 -1.88926386e-01 1.06154451e-01 2.21756758e-01 9.12063473e-02 -1.64549184e-01 5.68590399e-02 -7.84679868e-03 3.89763703e-04] Err = [0.2, 8.7287894882406736] **************************************************************** Lambda = 0.201 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.56113742e-02 -5.25683180e-01 -1.88850420e-01 1.05699150e-01 2.21575164e-01 9.14986515e-02 -1.64658362e-01 5.68775807e-02 -7.84828288e-03 3.89808169e-04] Err = [0.201, 8.728715091533795] **************************************************************** Lambda = 0.202 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.58443953e-02 -5.24585628e-01 -1.88773474e-01 1.05247610e-01 2.21393995e-01 9.17882010e-02 -1.64766051e-01 5.68957709e-02 -7.84972778e-03 3.89850925e-04] Err = [0.202, 8.7286425227005768] **************************************************************** Lambda = 0.203 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.60761474e-02 -5.23494744e-01 -1.88695572e-01 1.04799899e-01 2.21213345e-01 9.20748186e-02 -1.64872154e-01 5.69135869e-02 -7.85113066e-03 3.89891845e-04] Err = [0.203, 8.7285718729763513] **************************************************************** Lambda = 0.204 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.63066287e-02 -5.22410280e-01 -1.88616730e-01 1.04355629e-01 2.21032863e-01 9.23592564e-02 -1.64977078e-01 5.69311281e-02 -7.85250308e-03 3.89931451e-04] Err = [0.204, 8.7285026986478425] **************************************************************** Lambda = 0.205 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.65358679e-02 -5.21332384e-01 -1.88536954e-01 1.03915182e-01 2.20852977e-01 9.26406545e-02 -1.65080361e-01 5.69482809e-02 -7.85383178e-03 3.89969143e-04] Err = [0.205, 8.7284354924477636] **************************************************************** Lambda = 0.206 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.67638728e-02 -5.20260919e-01 -1.88456236e-01 1.03478399e-01 2.20673489e-01 9.29193685e-02 -1.65182186e-01 5.69650896e-02 -7.85512184e-03 3.90005150e-04] Err = [0.206, 8.728370071219647] **************************************************************** Lambda = 0.207 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.69906477e-02 -5.19195812e-01 -1.88374651e-01 1.03045193e-01 2.20494486e-01 9.31953959e-02 -1.65282570e-01 5.69815602e-02 -7.85637410e-03 3.90039512e-04] Err = [0.207, 8.7283063801969067] **************************************************************** Lambda = 0.208 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.72162045e-02 -5.18136929e-01 -1.88292158e-01 1.02615430e-01 2.20315735e-01 9.34690942e-02 -1.65381689e-01 5.69977337e-02 -7.85759319e-03 3.90072434e-04] Err = [0.208, 8.7282442478592692] **************************************************************** Lambda = 0.209 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.74405589e-02 -5.17084279e-01 -1.88208773e-01 1.02189225e-01 2.20137348e-01 9.37402237e-02 -1.65479413e-01 5.70135779e-02 -7.85877533e-03 3.90103745e-04] Err = [0.209, 8.7281838197757668] **************************************************************** Lambda = 0.21 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.76637022e-02 -5.16037701e-01 -1.88124613e-01 1.01766256e-01 2.19959362e-01 9.40090738e-02 -1.65575935e-01 5.70291444e-02 -7.85992683e-03 3.90133737e-04] Err = [0.21, 8.7281248189925282] **************************************************************** Lambda = 0.211 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.78856619e-02 -5.14997237e-01 -1.88039611e-01 1.01346762e-01 2.19781797e-01 9.42753579e-02 -1.65671073e-01 5.70443852e-02 -7.86104185e-03 3.90162139e-04] Err = [0.211, 8.7280674944114693] **************************************************************** Lambda = 0.212 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.81064703e-02 -5.13963029e-01 -1.87953738e-01 1.00931118e-01 2.19605066e-01 9.45382165e-02 -1.65764359e-01 5.70591848e-02 -7.86210682e-03 3.90188337e-04] Err = [0.212, 8.7280123380826282] **************************************************************** Lambda = 0.213 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.83260914e-02 -5.12934615e-01 -1.87867122e-01 1.00518454e-01 2.19428441e-01 9.47993484e-02 -1.65856731e-01 5.70737760e-02 -7.86314914e-03 3.90213575e-04] Err = [0.213, 8.7279583124673454] **************************************************************** Lambda = 0.214 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.85445620e-02 -5.11912143e-01 -1.87779690e-01 1.00109168e-01 2.19252278e-01 9.50579187e-02 -1.65947725e-01 5.70880425e-02 -7.86415506e-03 3.90237224e-04] Err = [0.214, 8.7279059313078324] **************************************************************** Lambda = 0.215 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.87618818e-02 -5.10895530e-01 -1.87691529e-01 9.97031510e-02 2.19076615e-01 9.53140148e-02 -1.66037405e-01 5.71020027e-02 -7.86512685e-03 3.90259394e-04] Err = [0.215, 8.7278550975172084] **************************************************************** Lambda = 0.216 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.89780674e-02 -5.09884710e-01 -1.87602582e-01 9.93004009e-02 2.18901299e-01 9.55677754e-02 -1.66125825e-01 5.71156667e-02 -7.86606555e-03 3.90280124e-04] Err = [0.216, 8.7278057842165513] **************************************************************** Lambda = 0.217 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.91931178e-02 -5.08879587e-01 -1.87512928e-01 9.89007451e-02 2.18726405e-01 9.58192926e-02 -1.66213059e-01 5.71290557e-02 -7.86697377e-03 3.90299539e-04] Err = [0.217, 8.7277578625093657] **************************************************************** Lambda = 0.218 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.94070425e-02 -5.07880126e-01 -1.87422594e-01 9.85041987e-02 2.18551959e-01 9.60685241e-02 -1.66299086e-01 5.71421644e-02 -7.86785092e-03 3.90317611e-04] Err = [0.218, 8.7277113631792531] **************************************************************** Lambda = 0.219 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.96198682e-02 -5.06886281e-01 -1.87331448e-01 9.81108621e-02 2.18377707e-01 9.63155966e-02 -1.66383927e-01 5.71549926e-02 -7.86869657e-03 3.90334309e-04] Err = [0.219, 8.7276663253492188] **************************************************************** Lambda = 0.22 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -6.98315901e-02 -5.05898062e-01 -1.87239673e-01 9.77206687e-02 2.18204180e-01 9.65600224e-02 -1.66467384e-01 5.71674991e-02 -7.86950640e-03 3.90349452e-04] Err = [0.22, 8.7276228525623605] **************************************************************** Lambda = 0.221 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.00422298e-02 -5.04915418e-01 -1.87147176e-01 9.73337001e-02 2.18031123e-01 9.68019683e-02 -1.66549508e-01 5.71796913e-02 -7.87028097e-03 3.90363057e-04] Err = [0.221, 8.7275809590159952] **************************************************************** Lambda = 0.222 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.02517681e-02 -5.03938056e-01 -1.87054030e-01 9.69494128e-02 2.17858115e-01 9.70424512e-02 -1.66630861e-01 5.71917090e-02 -7.87103671e-03 3.90375868e-04] Err = [0.222, 8.7275400065103774] **************************************************************** Lambda = 0.223 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.04602536e-02 -5.02966353e-01 -1.86960229e-01 9.65686067e-02 2.17686116e-01 9.72795940e-02 -1.66710441e-01 5.72033072e-02 -7.87174505e-03 3.90386596e-04] Err = [0.223, 8.7275010675070153] **************************************************************** Lambda = 0.224 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.06676554e-02 -5.01999760e-01 -1.86865748e-01 9.61903320e-02 2.17513897e-01 9.75156818e-02 -1.66789451e-01 5.72147777e-02 -7.87243986e-03 3.90396764e-04] Err = [0.224, 8.7274628791431859] **************************************************************** Lambda = 0.225 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.08740153e-02 -5.01038690e-01 -1.86770668e-01 9.58153827e-02 2.17342703e-01 9.77485573e-02 -1.66866770e-01 5.72258504e-02 -7.87308986e-03 3.90404969e-04] Err = [0.225, 8.7274265814482987] **************************************************************** Lambda = 0.226 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.10793139e-02 -5.00082730e-01 -1.86674965e-01 9.54430911e-02 2.17171549e-01 9.79799624e-02 -1.66943307e-01 5.72367443e-02 -7.87372043e-03 3.90412350e-04] Err = [0.226, 8.7273912415615502] **************************************************************** Lambda = 0.227 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.12835645e-02 -4.99131897e-01 -1.86578651e-01 9.50735221e-02 2.17000654e-01 9.82095726e-02 -1.67018897e-01 5.72474204e-02 -7.87432706e-03 3.90418704e-04] Err = [0.227, 8.7273570135392262] **************************************************************** Lambda = 0.228 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.14867971e-02 -4.98186388e-01 -1.86481750e-01 9.47071320e-02 2.16830579e-01 9.84363135e-02 -1.67092970e-01 5.72577395e-02 -7.87489354e-03 3.90423302e-04] Err = [0.228, 8.7273245069672871] **************************************************************** Lambda = 0.229 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.16890076e-02 -4.97245978e-01 -1.86384235e-01 9.43435654e-02 2.16660872e-01 9.86610138e-02 -1.67165959e-01 5.72678059e-02 -7.87543195e-03 3.90426683e-04] Err = [0.229, 8.7272932607704607] **************************************************************** Lambda = 0.23 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.18901996e-02 -4.96310627e-01 -1.86286166e-01 9.39827752e-02 2.16491640e-01 9.88836097e-02 -1.67237845e-01 5.72776173e-02 -7.87594211e-03 3.90428846e-04] Err = [0.23, 8.7272632813968478] **************************************************************** Lambda = 0.231 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.20903916e-02 -4.95380384e-01 -1.86187534e-01 9.36249389e-02 2.16323034e-01 9.91037468e-02 -1.67308433e-01 5.72871246e-02 -7.87641826e-03 3.90429526e-04] Err = [0.231, 8.7272347801767154] **************************************************************** Lambda = 0.232 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.22895587e-02 -4.94454867e-01 -1.86088370e-01 9.32693818e-02 2.16154301e-01 9.93229311e-02 -1.67378528e-01 5.72965248e-02 -7.87688337e-03 3.90429761e-04] Err = [0.232, 8.7272068910113596] **************************************************************** Lambda = 0.233 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.24877463e-02 -4.93534389e-01 -1.85988646e-01 9.29167590e-02 2.15986294e-01 9.95395305e-02 -1.67447259e-01 5.73056054e-02 -7.87731261e-03 3.90428429e-04] Err = [0.233, 8.727180533319471] **************************************************************** Lambda = 0.234 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.26849554e-02 -4.92618859e-01 -1.85888390e-01 9.25669800e-02 2.15818839e-01 9.97538416e-02 -1.67514783e-01 5.73144036e-02 -7.87771035e-03 3.90425728e-04] Err = [0.234, 8.7271555587478176] **************************************************************** Lambda = 0.235 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.28811772e-02 -4.91708073e-01 -1.85787627e-01 9.22196718e-02 2.15651660e-01 9.99665272e-02 -1.67581463e-01 5.73230097e-02 -7.87808712e-03 3.90422134e-04] Err = [0.235, 8.7271315439707688] **************************************************************** Lambda = 0.236 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.30764291e-02 -4.90802088e-01 -1.85686362e-01 9.18750238e-02 2.15484933e-01 1.00177201e-01 -1.67647088e-01 5.73313716e-02 -7.87843686e-03 3.90417372e-04] Err = [0.236, 8.727108735735186] **************************************************************** Lambda = 0.237 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.32707166e-02 -4.89900808e-01 -1.85584580e-01 9.15329275e-02 2.15318513e-01 1.00386113e-01 -1.67711787e-01 5.73395195e-02 -7.87876300e-03 3.90411595e-04] Err = [0.237, 8.7270869910960869] **************************************************************** Lambda = 0.238 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.34640539e-02 -4.89004288e-01 -1.85482310e-01 9.11935256e-02 2.15152658e-01 1.00592835e-01 -1.67775337e-01 5.73474004e-02 -7.87905942e-03 3.90404529e-04] Err = [0.238, 8.727066541908691] **************************************************************** Lambda = 0.239 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.36564357e-02 -4.88112379e-01 -1.85379584e-01 9.08565615e-02 2.14987198e-01 1.00797803e-01 -1.67837983e-01 5.73550746e-02 -7.87933320e-03 3.90396494e-04] Err = [0.239, 8.7270470988877804] **************************************************************** Lambda = 0.24 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.38478683e-02 -4.87225001e-01 -1.85276382e-01 9.05219823e-02 2.14821902e-01 1.01001322e-01 -1.67899870e-01 5.73625759e-02 -7.87958816e-03 3.90387659e-04] Err = [0.24, 8.7270285392261915] **************************************************************** Lambda = 0.241 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.40383959e-02 -4.86342486e-01 -1.85172709e-01 9.01904598e-02 2.14657749e-01 1.01201615e-01 -1.67960063e-01 5.73696772e-02 -7.87979791e-03 3.90376836e-04] Err = [0.241, 8.7270118453330188] **************************************************************** Lambda = 0.242 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.42279538e-02 -4.85464090e-01 -1.85068601e-01 8.98606121e-02 2.14493030e-01 1.01401963e-01 -1.68020306e-01 5.73768034e-02 -7.88001193e-03 3.90366255e-04] Err = [0.242, 8.7269951462783624] **************************************************************** Lambda = 0.243 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.44166330e-02 -4.84590536e-01 -1.84963989e-01 8.95339529e-02 2.14329467e-01 1.01598913e-01 -1.68078743e-01 5.73835002e-02 -7.88017713e-03 3.90353518e-04] Err = [0.243, 8.7269804532013922] **************************************************************** Lambda = 0.244 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.46043756e-02 -4.83721282e-01 -1.84859007e-01 8.92093760e-02 2.14166068e-01 1.01794703e-01 -1.68136605e-01 5.73900716e-02 -7.88032922e-03 3.90340243e-04] Err = [0.244, 8.7269663966292406] **************************************************************** Lambda = 0.245 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.47912161e-02 -4.82856475e-01 -1.84753587e-01 8.88872722e-02 2.14003180e-01 1.01988520e-01 -1.68193438e-01 5.73964048e-02 -7.88045491e-03 3.90325826e-04] Err = [0.245, 8.7269534824231929] **************************************************************** Lambda = 0.246 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.49771562e-02 -4.81996048e-01 -1.84647755e-01 8.85675592e-02 2.13840732e-01 1.02180528e-01 -1.68249333e-01 5.74025223e-02 -7.88055681e-03 3.90310386e-04] Err = [0.246, 8.7269416099028518] **************************************************************** Lambda = 0.247 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.51622057e-02 -4.81139975e-01 -1.84541506e-01 8.82502565e-02 2.13678734e-01 1.02370685e-01 -1.68304264e-01 5.74084169e-02 -7.88063407e-03 3.90293882e-04] Err = [0.247, 8.7269308111138297] **************************************************************** Lambda = 0.248 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.53463665e-02 -4.80288164e-01 -1.84434836e-01 8.79352469e-02 2.13516998e-01 1.02559309e-01 -1.68358394e-01 5.74141280e-02 -7.88069119e-03 3.90276516e-04] Err = [0.248, 8.7269209215780013] **************************************************************** Lambda = 0.249 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.55296391e-02 -4.79440583e-01 -1.84327811e-01 8.76224563e-02 2.13355703e-01 1.02746279e-01 -1.68411684e-01 5.74196484e-02 -7.88072755e-03 3.90258265e-04] Err = [0.249, 8.7269119415275735] **************************************************************** Lambda = 0.25 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.57120489e-02 -4.78597305e-01 -1.84220375e-01 8.73121361e-02 2.13194986e-01 1.02931165e-01 -1.68463883e-01 5.74249149e-02 -7.88073557e-03 3.90238782e-04] Err = [0.25, 8.7269041637991052] **************************************************************** Lambda = 0.251 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.58935873e-02 -4.77758215e-01 -1.84112584e-01 8.70040687e-02 2.13034706e-01 1.03114359e-01 -1.68515215e-01 5.74299832e-02 -7.88072189e-03 3.90218370e-04] Err = [0.251, 8.7268973460385268] **************************************************************** Lambda = 0.252 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.60742621e-02 -4.76923233e-01 -1.84004405e-01 8.66981971e-02 2.12874686e-01 1.03296088e-01 -1.68565784e-01 5.74348774e-02 -7.88068917e-03 3.90197145e-04] Err = [0.252, 8.7268913784720059] **************************************************************** Lambda = 0.253 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.62540765e-02 -4.76092314e-01 -1.83895861e-01 8.63944477e-02 2.12714981e-01 1.03476357e-01 -1.68615606e-01 5.74396020e-02 -7.88063799e-03 3.90175134e-04] Err = [0.253, 8.7268862212192353] **************************************************************** Lambda = 0.254 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.64330366e-02 -4.75265487e-01 -1.83787007e-01 8.60928916e-02 2.12555788e-01 1.03654895e-01 -1.68664549e-01 5.74441266e-02 -7.88056494e-03 3.90152188e-04] Err = [0.254, 8.7268820139032126] **************************************************************** Lambda = 0.255 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.66111726e-02 -4.74442836e-01 -1.83677763e-01 8.57938136e-02 2.12397277e-01 1.03831183e-01 -1.68712312e-01 5.74483747e-02 -7.88046087e-03 3.90127886e-04] Err = [0.255, 8.7268790973815449] **************************************************************** Lambda = 0.256 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.67884667e-02 -4.73624129e-01 -1.83568158e-01 8.54967988e-02 2.12238955e-01 1.04006193e-01 -1.68759413e-01 5.74524730e-02 -7.88034056e-03 3.90102897e-04] Err = [0.256, 8.7268769198902856] **************************************************************** Lambda = 0.257 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.69649121e-02 -4.72809296e-01 -1.83458265e-01 8.52016854e-02 2.12080870e-01 1.04180047e-01 -1.68805944e-01 5.74564467e-02 -7.88020715e-03 3.90077367e-04] Err = [0.257, 8.7268753518227804] **************************************************************** Lambda = 0.258 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.71405515e-02 -4.71998569e-01 -1.83348028e-01 8.49090350e-02 2.11923567e-01 1.04351547e-01 -1.68851248e-01 5.74601330e-02 -7.88004150e-03 3.90050427e-04] Err = [0.258, 8.726875114433275] **************************************************************** Lambda = 0.259 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.73153537e-02 -4.71191653e-01 -1.83237522e-01 8.46182404e-02 2.11766551e-01 1.04521867e-01 -1.68895974e-01 5.74636930e-02 -7.87986256e-03 3.90022939e-04] Err = [0.259, 8.7268754717445667] **************************************************************** Lambda = 0.26 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.74893600e-02 -4.70388661e-01 -1.83126600e-01 8.43297321e-02 2.11609845e-01 1.04690495e-01 -1.68939793e-01 5.74670403e-02 -7.87965982e-03 3.89994414e-04] Err = [0.26, 8.7268768645873944] **************************************************************** Lambda = 0.261 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.76625374e-02 -4.69589415e-01 -1.83015447e-01 8.40430295e-02 2.11453441e-01 1.04857974e-01 -1.68983057e-01 5.74702675e-02 -7.87944455e-03 3.89965375e-04] Err = [0.261, 8.7268788166510145] **************************************************************** Lambda = 0.262 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.78349075e-02 -4.68793987e-01 -1.82904025e-01 8.37583503e-02 2.11297494e-01 1.05023897e-01 -1.69025535e-01 5.74733169e-02 -7.87920992e-03 3.89935512e-04] Err = [0.262, 8.7268816111573777] **************************************************************** Lambda = 0.263 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.80065097e-02 -4.68002486e-01 -1.82792212e-01 8.34760816e-02 2.11142183e-01 1.05187614e-01 -1.69066842e-01 5.74760896e-02 -7.87894405e-03 3.89904277e-04] Err = [0.263, 8.7268856857494512] **************************************************************** Lambda = 0.264 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.81772885e-02 -4.67214574e-01 -1.82680208e-01 8.31954174e-02 2.10986999e-01 1.05350577e-01 -1.69107809e-01 5.74787954e-02 -7.87867189e-03 3.89872811e-04] Err = [0.264, 8.7268900998542254] **************************************************************** Lambda = 0.265 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.83473056e-02 -4.66430535e-01 -1.82567868e-01 8.29170980e-02 2.10832548e-01 1.05511295e-01 -1.69147600e-01 5.74812251e-02 -7.87836869e-03 3.89839985e-04] Err = [0.265, 8.7268957807208043] **************************************************************** Lambda = 0.266 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.85165127e-02 -4.65649993e-01 -1.82455305e-01 8.26403245e-02 2.10678083e-01 1.05671441e-01 -1.69187135e-01 5.74836066e-02 -7.87806124e-03 3.89807017e-04] Err = [0.266, 8.7269017162892908] **************************************************************** Lambda = 0.267 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.86849750e-02 -4.64873324e-01 -1.82342422e-01 8.23659818e-02 2.10524490e-01 1.05829095e-01 -1.69225364e-01 5.74856802e-02 -7.87771904e-03 3.89772521e-04] Err = [0.267, 8.7269090624502184] **************************************************************** Lambda = 0.268 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.88526547e-02 -4.64100155e-01 -1.82229258e-01 8.20933419e-02 2.10370951e-01 1.05985904e-01 -1.69263171e-01 5.74876624e-02 -7.87736737e-03 3.89737640e-04] Err = [0.268, 8.7269168538630844] **************************************************************** Lambda = 0.269 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.90195669e-02 -4.63330645e-01 -1.82115897e-01 8.18226839e-02 2.10218035e-01 1.06140983e-01 -1.69300113e-01 5.74894483e-02 -7.87699423e-03 3.89701841e-04] Err = [0.269, 8.7269255502008765] **************************************************************** Lambda = 0.27 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.91857179e-02 -4.62564683e-01 -1.82002277e-01 8.15538891e-02 2.10065481e-01 1.06294699e-01 -1.69336363e-01 5.74910779e-02 -7.87660409e-03 3.89665318e-04] Err = [0.27, 8.7269349647306544] **************************************************************** Lambda = 0.271 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.93511202e-02 -4.61802263e-01 -1.81888359e-01 8.12870260e-02 2.09913243e-01 1.06447022e-01 -1.69371892e-01 5.74925420e-02 -7.87619575e-03 3.89628014e-04] Err = [0.271, 8.7269451663618955] **************************************************************** Lambda = 0.272 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.95157831e-02 -4.61043439e-01 -1.81774194e-01 8.10222146e-02 2.09761591e-01 1.06597540e-01 -1.69406493e-01 5.74937919e-02 -7.87576365e-03 3.89589680e-04] Err = [0.272, 8.7269563496837801] **************************************************************** Lambda = 0.273 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.96796855e-02 -4.60288019e-01 -1.81659838e-01 8.07590503e-02 2.09610203e-01 1.06747029e-01 -1.69440598e-01 5.74949346e-02 -7.87532040e-03 3.89550891e-04] Err = [0.273, 8.7269680269840446] **************************************************************** Lambda = 0.274 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -7.98428100e-02 -4.59535822e-01 -1.81545326e-01 8.04971834e-02 2.09458721e-01 1.06896247e-01 -1.69474617e-01 5.74960713e-02 -7.87487784e-03 3.89512182e-04] Err = [0.274, 8.7269797506101465] **************************************************************** Lambda = 0.275 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.00052340e-02 -4.58787249e-01 -1.81430499e-01 8.02376199e-02 2.09307964e-01 1.07043207e-01 -1.69507442e-01 5.74969256e-02 -7.87440334e-03 3.89472067e-04] Err = [0.275, 8.7269927788282491] **************************************************************** Lambda = 0.276 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.01669332e-02 -4.58042153e-01 -1.81315477e-01 7.99799665e-02 2.09157896e-01 1.07188368e-01 -1.69539363e-01 5.74975731e-02 -7.87390605e-03 3.89430970e-04] Err = [0.276, 8.7270067248982439] **************************************************************** Lambda = 0.277 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.03279009e-02 -4.57300395e-01 -1.81200246e-01 7.97240398e-02 2.09008056e-01 1.07332437e-01 -1.69570735e-01 5.74980987e-02 -7.87339573e-03 3.89389327e-04] Err = [0.277, 8.7270212602740891] **************************************************************** Lambda = 0.278 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.04881475e-02 -4.56561967e-01 -1.81084796e-01 7.94698389e-02 2.08858624e-01 1.07475177e-01 -1.69601441e-01 5.74984743e-02 -7.87286914e-03 3.89346993e-04] Err = [0.278, 8.7270364568862835] **************************************************************** Lambda = 0.279 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.06476754e-02 -4.55826824e-01 -1.80969125e-01 7.92173469e-02 2.08709422e-01 1.07616815e-01 -1.69631591e-01 5.74987253e-02 -7.87232915e-03 3.89304094e-04] Err = [0.279, 8.7270522427823511] **************************************************************** Lambda = 0.28 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.08064727e-02 -4.55094922e-01 -1.80853339e-01 7.89663942e-02 2.08560579e-01 1.07757409e-01 -1.69661251e-01 5.74988724e-02 -7.87177847e-03 3.89260763e-04] Err = [0.28, 8.7270685028836112] **************************************************************** Lambda = 0.281 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.09646029e-02 -4.54366469e-01 -1.80737229e-01 7.87176580e-02 2.08412408e-01 1.07895835e-01 -1.69689757e-01 5.74987453e-02 -7.87119668e-03 3.89216059e-04] Err = [0.281, 8.7270860152188039] **************************************************************** Lambda = 0.282 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.11220076e-02 -4.53641155e-01 -1.80621002e-01 7.84703374e-02 2.08264479e-01 1.08033449e-01 -1.69717895e-01 5.74985436e-02 -7.87060757e-03 3.89171073e-04] Err = [0.282, 8.7271038509148564] **************************************************************** Lambda = 0.283 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.12787143e-02 -4.52919081e-01 -1.80504603e-01 7.82247474e-02 2.08116959e-01 1.08169732e-01 -1.69745367e-01 5.74981915e-02 -7.87000215e-03 3.89125394e-04] Err = [0.283, 8.727122382808604] **************************************************************** Lambda = 0.284 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.14347371e-02 -4.52200220e-01 -1.80387973e-01 7.79809212e-02 2.07969819e-01 1.08304643e-01 -1.69772133e-01 5.74976779e-02 -7.86937894e-03 3.89078949e-04] Err = [0.284, 8.7271416517140246] **************************************************************** Lambda = 0.285 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.15900538e-02 -4.51484455e-01 -1.80271223e-01 7.77385449e-02 2.07822974e-01 1.08438626e-01 -1.69798466e-01 5.74970729e-02 -7.86874639e-03 3.89032129e-04] Err = [0.285, 8.7271613150156373] **************************************************************** Lambda = 0.286 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.17447018e-02 -4.50771950e-01 -1.80154284e-01 7.74980648e-02 2.07676780e-01 1.08570809e-01 -1.69823879e-01 5.74962549e-02 -7.86809017e-03 3.88984281e-04] Err = [0.286, 8.7271819468978542] **************************************************************** Lambda = 0.287 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.18986411e-02 -4.50062349e-01 -1.80037189e-01 7.72587833e-02 2.07530370e-01 1.08702868e-01 -1.69849263e-01 5.74954418e-02 -7.86743565e-03 3.88936551e-04] Err = [0.287, 8.7272025697774129] **************************************************************** Lambda = 0.288 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.20519311e-02 -4.49356016e-01 -1.79919888e-01 7.70214936e-02 2.07384759e-01 1.08832838e-01 -1.69873570e-01 5.74943768e-02 -7.86675286e-03 3.88887583e-04] Err = [0.288, 8.7272243236412415] **************************************************************** Lambda = 0.289 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.22045273e-02 -4.48652643e-01 -1.79802483e-01 7.67855327e-02 2.07239292e-01 1.08962159e-01 -1.69897587e-01 5.74932552e-02 -7.86606474e-03 3.88838420e-04] Err = [0.289, 8.7272463292803764] **************************************************************** Lambda = 0.29 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.23564798e-02 -4.47952452e-01 -1.79684870e-01 7.65514856e-02 2.07094461e-01 1.09089641e-01 -1.69920652e-01 5.74919111e-02 -7.86535172e-03 3.88788168e-04] Err = [0.29, 8.7272693386479148] **************************************************************** Lambda = 0.291 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.25077595e-02 -4.47255259e-01 -1.79567142e-01 7.63189132e-02 2.06949982e-01 1.09216075e-01 -1.69943214e-01 5.74904578e-02 -7.86462721e-03 3.88737443e-04] Err = [0.291, 8.7272928309039717] **************************************************************** Lambda = 0.292 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.26583819e-02 -4.46561051e-01 -1.79449238e-01 7.60878952e-02 2.06805804e-01 1.09341403e-01 -1.69965221e-01 5.74888801e-02 -7.86388926e-03 3.88686148e-04] Err = [0.292, 8.7273168801567085] **************************************************************** Lambda = 0.293 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.28083353e-02 -4.45869756e-01 -1.79331225e-01 7.58582562e-02 2.06661846e-01 1.09465917e-01 -1.69986847e-01 5.74872222e-02 -7.86314318e-03 3.88634529e-04] Err = [0.293, 8.7273412821854581] **************************************************************** Lambda = 0.294 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.29576618e-02 -4.45181573e-01 -1.79213040e-01 7.56304946e-02 2.06518640e-01 1.09588485e-01 -1.70007473e-01 5.74853315e-02 -7.86237103e-03 3.88581771e-04] Err = [0.294, 8.7273667184050847] **************************************************************** Lambda = 0.295 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.31063321e-02 -4.44496263e-01 -1.79094723e-01 7.54041249e-02 2.06375620e-01 1.09710244e-01 -1.70027711e-01 5.74833580e-02 -7.86159036e-03 3.88528668e-04] Err = [0.295, 8.7273925336279881] **************************************************************** Lambda = 0.296 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.32543485e-02 -4.43813812e-01 -1.78976299e-01 7.51791301e-02 2.06232845e-01 1.09831146e-01 -1.70047543e-01 5.74812979e-02 -7.86080077e-03 3.88475204e-04] Err = [0.296, 8.727418723675985] **************************************************************** Lambda = 0.297 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.34017241e-02 -4.43134238e-01 -1.78857740e-01 7.49556019e-02 2.06090375e-01 1.09951015e-01 -1.70066866e-01 5.74791254e-02 -7.85999918e-03 3.88421237e-04] Err = [0.297, 8.7274454186155364] **************************************************************** Lambda = 0.298 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.35484680e-02 -4.42457588e-01 -1.78739079e-01 7.47336424e-02 2.05948456e-01 1.10069479e-01 -1.70085495e-01 5.74767962e-02 -7.85918051e-03 3.88366541e-04] Err = [0.298, 8.7274727957264506] **************************************************************** Lambda = 0.299 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.36945825e-02 -4.41783757e-01 -1.78620254e-01 7.45131379e-02 2.05806742e-01 1.10187009e-01 -1.70103654e-01 5.74743624e-02 -7.85835063e-03 3.88311374e-04] Err = [0.299, 8.7275006407501365] **************************************************************** Lambda = 0.3 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.38400856e-02 -4.41112865e-01 -1.78501296e-01 7.42943248e-02 2.05665668e-01 1.10302886e-01 -1.70120976e-01 5.74717358e-02 -7.85749937e-03 3.88255280e-04] Err = [0.3, 8.7275293447745863] **************************************************************** Lambda = 0.301 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.39849431e-02 -4.40444672e-01 -1.78382275e-01 7.40766835e-02 2.05524732e-01 1.10418219e-01 -1.70138068e-01 5.74690665e-02 -7.85664436e-03 3.88199059e-04] Err = [0.301, 8.7275582191192509] **************************************************************** Lambda = 0.302 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.41291903e-02 -4.39779324e-01 -1.78263126e-01 7.38606142e-02 2.05384270e-01 1.10532197e-01 -1.70154478e-01 5.74662418e-02 -7.85577229e-03 3.88142106e-04] Err = [0.302, 8.727587786012462] **************************************************************** Lambda = 0.303 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.42728202e-02 -4.39116731e-01 -1.78143865e-01 7.36459449e-02 2.05244124e-01 1.10645170e-01 -1.70170395e-01 5.74633085e-02 -7.85488864e-03 3.88084668e-04] Err = [0.303, 8.7276178278092011] **************************************************************** Lambda = 0.304 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.44158195e-02 -4.38456785e-01 -1.78024531e-01 7.34324474e-02 2.05104106e-01 1.10757587e-01 -1.70186071e-01 5.74603288e-02 -7.85400074e-03 3.88027078e-04] Err = [0.304, 8.7276480565430443] **************************************************************** Lambda = 0.305 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.45582430e-02 -4.37799740e-01 -1.77905029e-01 7.32207728e-02 2.04964837e-01 1.10868051e-01 -1.70200734e-01 5.74571114e-02 -7.85308607e-03 3.87968314e-04] Err = [0.305, 8.727679337024334] **************************************************************** Lambda = 0.306 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.47000337e-02 -4.37145273e-01 -1.77785495e-01 7.30101527e-02 2.04825629e-01 1.10978164e-01 -1.70215273e-01 5.74538776e-02 -7.85217072e-03 3.87909561e-04] Err = [0.306, 8.7277106814395768] **************************************************************** Lambda = 0.307 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.48412354e-02 -4.36493547e-01 -1.77665828e-01 7.28010524e-02 2.04686879e-01 1.11086958e-01 -1.70229145e-01 5.74504913e-02 -7.85123858e-03 3.87850086e-04] Err = [0.307, 8.727742694688196] **************************************************************** Lambda = 0.308 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.49818210e-02 -4.35844426e-01 -1.77546131e-01 7.25931261e-02 2.04548359e-01 1.11195082e-01 -1.70242722e-01 5.74470466e-02 -7.85030087e-03 3.87790401e-04] Err = [0.308, 8.7277749491944192] **************************************************************** Lambda = 0.309 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.51218399e-02 -4.35198061e-01 -1.77426253e-01 7.23868628e-02 2.04410369e-01 1.11301629e-01 -1.70255479e-01 5.74434101e-02 -7.84934162e-03 3.87729774e-04] Err = [0.309, 8.7278080522760408] **************************************************************** Lambda = 0.31 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.52612453e-02 -4.34554260e-01 -1.77306379e-01 7.21817074e-02 2.04272663e-01 1.11407513e-01 -1.70267958e-01 5.74397203e-02 -7.84837748e-03 3.87668972e-04] Err = [0.31, 8.7278413661179215] **************************************************************** Lambda = 0.311 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.54000649e-02 -4.33913035e-01 -1.77186376e-01 7.19778622e-02 2.04135121e-01 1.11512602e-01 -1.70280041e-01 5.74359437e-02 -7.84740413e-03 3.87607786e-04] Err = [0.311, 8.7278750657591928] **************************************************************** Lambda = 0.312 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.55383011e-02 -4.33274449e-01 -1.77066330e-01 7.17753869e-02 2.03998115e-01 1.11616446e-01 -1.70291523e-01 5.74320332e-02 -7.84641634e-03 3.87545989e-04] Err = [0.312, 8.7279093282015126] **************************************************************** Lambda = 0.313 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.56759726e-02 -4.32638494e-01 -1.76946151e-01 7.15743944e-02 2.03861532e-01 1.11719017e-01 -1.70302355e-01 5.74279735e-02 -7.84541209e-03 3.87483480e-04] Err = [0.313, 8.7279442422726525] **************************************************************** Lambda = 0.314 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.58130702e-02 -4.32005117e-01 -1.76825893e-01 7.13747385e-02 2.03725362e-01 1.11820491e-01 -1.70312651e-01 5.74237944e-02 -7.84439495e-03 3.87420428e-04] Err = [0.314, 8.7279796738821425] **************************************************************** Lambda = 0.315 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.59495858e-02 -4.31374230e-01 -1.76705571e-01 7.11762712e-02 2.03589370e-01 1.11921284e-01 -1.70322629e-01 5.74195491e-02 -7.84337114e-03 3.87357110e-04] Err = [0.315, 8.7280153868796404] **************************************************************** Lambda = 0.316 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.60854979e-02 -4.30745714e-01 -1.76585260e-01 7.09786950e-02 2.03453380e-01 1.12021922e-01 -1.70332592e-01 5.74153137e-02 -7.84234972e-03 3.87293942e-04] Err = [0.316, 8.7280510260635307] **************************************************************** Lambda = 0.317 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.62208667e-02 -4.30119836e-01 -1.76464846e-01 7.07826853e-02 2.03318097e-01 1.12120871e-01 -1.70341698e-01 5.74108798e-02 -7.84130614e-03 3.87229808e-04] Err = [0.317, 8.7280875251789318] **************************************************************** Lambda = 0.318 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.63556746e-02 -4.29496449e-01 -1.76344350e-01 7.05879673e-02 2.03183111e-01 1.12218881e-01 -1.70350342e-01 5.74063435e-02 -7.84025159e-03 3.87165214e-04] Err = [0.318, 8.7281244691115543] **************************************************************** Lambda = 0.319 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.64899248e-02 -4.28875555e-01 -1.76223797e-01 7.03945380e-02 2.03048553e-01 1.12315808e-01 -1.70358459e-01 5.74016903e-02 -7.83918447e-03 3.87100088e-04] Err = [0.319, 8.7281619064728826] **************************************************************** Lambda = 0.32 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.66236146e-02 -4.28257105e-01 -1.76103193e-01 7.02023159e-02 2.02914307e-01 1.12411864e-01 -1.70366162e-01 5.73969475e-02 -7.83810796e-03 3.87034574e-04] Err = [0.32, 8.7281997242825931] **************************************************************** Lambda = 0.321 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.67567432e-02 -4.27641033e-01 -1.75982528e-01 7.00112169e-02 2.02780223e-01 1.12507291e-01 -1.70373574e-01 5.73921441e-02 -7.83702537e-03 3.86968821e-04] Err = [0.321, 8.7282377841598571] **************************************************************** Lambda = 0.322 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.68893249e-02 -4.27027422e-01 -1.75861818e-01 6.98214148e-02 2.02646582e-01 1.12601607e-01 -1.70380443e-01 5.73872198e-02 -7.83592973e-03 3.86902515e-04] Err = [0.322, 8.7282763606644398] **************************************************************** Lambda = 0.323 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.70213536e-02 -4.26416173e-01 -1.75741052e-01 6.96327418e-02 2.02513150e-01 1.12695228e-01 -1.70386987e-01 5.73822271e-02 -7.83482710e-03 3.86835929e-04] Err = [0.323, 8.7283152245919311] **************************************************************** Lambda = 0.324 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.71528486e-02 -4.25807424e-01 -1.75620270e-01 6.94454549e-02 2.02380451e-01 1.12787317e-01 -1.70392780e-01 5.73770640e-02 -7.83370577e-03 3.86768537e-04] Err = [0.324, 8.7283548068691736] **************************************************************** Lambda = 0.325 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.72837905e-02 -4.25200924e-01 -1.75499404e-01 6.92591668e-02 2.02247651e-01 1.12879175e-01 -1.70398478e-01 5.73718865e-02 -7.83258360e-03 3.86701137e-04] Err = [0.325, 8.7283944408650438] **************************************************************** Lambda = 0.326 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.74141951e-02 -4.24596806e-01 -1.75378507e-01 6.90740951e-02 2.02115271e-01 1.12970012e-01 -1.70403685e-01 5.73666009e-02 -7.83144989e-03 3.86633253e-04] Err = [0.326, 8.728434530005897] **************************************************************** Lambda = 0.327 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.75440569e-02 -4.23994998e-01 -1.75257593e-01 6.88901092e-02 2.01983200e-01 1.13060081e-01 -1.70408539e-01 5.73612413e-02 -7.83030862e-03 3.86565064e-04] Err = [0.327, 8.7284749071591072] **************************************************************** Lambda = 0.328 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.76734015e-02 -4.23395586e-01 -1.75136604e-01 6.87074759e-02 2.01851593e-01 1.13148917e-01 -1.70412774e-01 5.73557401e-02 -7.82915176e-03 3.86496204e-04] Err = [0.328, 8.7285159086182471] **************************************************************** Lambda = 0.329 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.78022097e-02 -4.22798437e-01 -1.75015584e-01 6.85258973e-02 2.01720221e-01 1.13237084e-01 -1.70416703e-01 5.73501753e-02 -7.82798849e-03 3.86427088e-04] Err = [0.329, 8.7285571492365897] **************************************************************** Lambda = 0.33 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.79304675e-02 -4.22203504e-01 -1.74894609e-01 6.83452213e-02 2.01589040e-01 1.13324821e-01 -1.70420473e-01 5.73445858e-02 -7.82682352e-03 3.86357937e-04] Err = [0.33, 8.7285984639865166] **************************************************************** Lambda = 0.331 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.80582460e-02 -4.21611015e-01 -1.74773473e-01 6.81661686e-02 2.01458510e-01 1.13410784e-01 -1.70423310e-01 5.73387746e-02 -7.82563339e-03 3.86287674e-04] Err = [0.331, 8.7286407568125419] **************************************************************** Lambda = 0.332 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.81854858e-02 -4.21020706e-01 -1.74652344e-01 6.79880370e-02 2.01328104e-01 1.13496349e-01 -1.70425992e-01 5.73329377e-02 -7.82444131e-03 3.86217359e-04] Err = [0.332, 8.7286831329912697] **************************************************************** Lambda = 0.333 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.83121824e-02 -4.20432576e-01 -1.74531284e-01 6.78107766e-02 2.01197935e-01 1.13581460e-01 -1.70428510e-01 5.73270751e-02 -7.82324749e-03 3.86147008e-04] Err = [0.333, 8.72872558493615] **************************************************************** Lambda = 0.334 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.84383876e-02 -4.19846733e-01 -1.74410101e-01 6.76348469e-02 2.01068149e-01 1.13665396e-01 -1.70430421e-01 5.73210716e-02 -7.82203795e-03 3.86075973e-04] Err = [0.334, 8.7287686362325729] **************************************************************** Lambda = 0.335 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.85640674e-02 -4.19263092e-01 -1.74288963e-01 6.74599149e-02 2.00938711e-01 1.13748608e-01 -1.70432016e-01 5.73150044e-02 -7.82082215e-03 3.86004695e-04] Err = [0.335, 8.7288119369165393] **************************************************************** Lambda = 0.336 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.86892474e-02 -4.18681677e-01 -1.74167764e-01 6.72861593e-02 2.00809641e-01 1.13830834e-01 -1.70433124e-01 5.73088279e-02 -7.81959448e-03 3.85932911e-04] Err = [0.336, 8.7288556877286201] **************************************************************** Lambda = 0.337 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.88139110e-02 -4.18102377e-01 -1.74046538e-01 6.71133578e-02 2.00680631e-01 1.13912666e-01 -1.70434063e-01 5.73026201e-02 -7.81836408e-03 3.85861036e-04] Err = [0.337, 8.7288995624645356] **************************************************************** Lambda = 0.338 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.89380748e-02 -4.17525307e-01 -1.73925322e-01 6.69417159e-02 2.00552149e-01 1.13993376e-01 -1.70434466e-01 5.72962933e-02 -7.81712087e-03 3.85788619e-04] Err = [0.338, 8.7289439271700182] **************************************************************** Lambda = 0.339 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.90617311e-02 -4.16950360e-01 -1.73804098e-01 6.67710537e-02 2.00423905e-01 1.14073459e-01 -1.70434584e-01 5.72899083e-02 -7.81587184e-03 3.85715973e-04] Err = [0.339, 8.7289885070359734] **************************************************************** Lambda = 0.34 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.91849077e-02 -4.16377641e-01 -1.73682819e-01 6.66016698e-02 2.00296172e-01 1.14152282e-01 -1.70434071e-01 5.72833782e-02 -7.81460677e-03 3.85642632e-04] Err = [0.34, 8.7290337055987219] **************************************************************** Lambda = 0.341 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.93075718e-02 -4.15806965e-01 -1.73561549e-01 6.64331338e-02 2.00168501e-01 1.14230813e-01 -1.70433453e-01 5.72768337e-02 -7.81334100e-03 3.85569294e-04] Err = [0.341, 8.7290789368730586] **************************************************************** Lambda = 0.342 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.94297621e-02 -4.15238491e-01 -1.73440229e-01 6.62658656e-02 2.00041343e-01 1.14308088e-01 -1.70432204e-01 5.72701445e-02 -7.81205922e-03 3.85495262e-04] Err = [0.342, 8.729124785449331] **************************************************************** Lambda = 0.343 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.95514349e-02 -4.14672047e-01 -1.73318999e-01 6.60993575e-02 1.99914410e-01 1.14385002e-01 -1.70430843e-01 5.72634424e-02 -7.81077716e-03 3.85421260e-04] Err = [0.343, 8.7291706426900504] **************************************************************** Lambda = 0.344 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.96726171e-02 -4.14107638e-01 -1.73197730e-01 6.59338089e-02 1.99787576e-01 1.14461433e-01 -1.70429260e-01 5.72566949e-02 -7.80949062e-03 3.85347083e-04] Err = [0.344, 8.7292166677825929] **************************************************************** Lambda = 0.345 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.97933419e-02 -4.13545422e-01 -1.73076391e-01 6.57695947e-02 1.99661320e-01 1.14536446e-01 -1.70426954e-01 5.72497793e-02 -7.80818528e-03 3.85272086e-04] Err = [0.345, 8.7292634194587588] **************************************************************** Lambda = 0.346 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -8.99135673e-02 -4.12985223e-01 -1.72955113e-01 6.56062241e-02 1.99535316e-01 1.14610958e-01 -1.70424448e-01 5.72428279e-02 -7.80687686e-03 3.85196987e-04] Err = [0.346, 8.7293102809554952] **************************************************************** Lambda = 0.347 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.00333069e-02 -4.12427035e-01 -1.72833831e-01 6.54437788e-02 1.99409499e-01 1.14684927e-01 -1.70421701e-01 5.72358277e-02 -7.80556368e-03 3.85121704e-04] Err = [0.347, 8.7293573248453171] **************************************************************** Lambda = 0.348 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.01525648e-02 -4.11870872e-01 -1.72712564e-01 6.52822929e-02 1.99283961e-01 1.14758222e-01 -1.70418647e-01 5.72287635e-02 -7.80424400e-03 3.85046161e-04] Err = [0.348, 8.7294046158825367] **************************************************************** Lambda = 0.349 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.02713741e-02 -4.11316837e-01 -1.72591236e-01 6.51220796e-02 1.99158984e-01 1.14830166e-01 -1.70414907e-01 5.72215402e-02 -7.80290657e-03 3.84969844e-04] Err = [0.349, 8.7294525841187109] **************************************************************** Lambda = 0.35 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.03896928e-02 -4.10764744e-01 -1.72469958e-01 6.49626518e-02 1.99034149e-01 1.14901773e-01 -1.70411048e-01 5.72143000e-02 -7.80156819e-03 3.84893519e-04] Err = [0.35, 8.7295005850438407] **************************************************************** Lambda = 0.351 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.05075551e-02 -4.10214691e-01 -1.72348643e-01 6.48043353e-02 1.98909703e-01 1.14972390e-01 -1.70406699e-01 5.72069491e-02 -7.80021771e-03 3.84816677e-04] Err = [0.351, 8.729549045344811] **************************************************************** Lambda = 0.352 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.06249235e-02 -4.09666527e-01 -1.72227405e-01 6.46467120e-02 1.98785322e-01 1.15042859e-01 -1.70402337e-01 5.71996074e-02 -7.79886938e-03 3.84739967e-04] Err = [0.352, 8.7295974188574395] **************************************************************** Lambda = 0.353 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.07418447e-02 -4.09120405e-01 -1.72106129e-01 6.44902307e-02 1.98661417e-01 1.15112198e-01 -1.70397414e-01 5.71921376e-02 -7.79750694e-03 3.84662649e-04] Err = [0.353, 8.7296463323509883] **************************************************************** Lambda = 0.354 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.08582948e-02 -4.08576217e-01 -1.71984894e-01 6.43346185e-02 1.98537771e-01 1.15180965e-01 -1.70392242e-01 5.71846186e-02 -7.79613976e-03 3.84585151e-04] Err = [0.354, 8.7296954133452278] **************************************************************** Lambda = 0.355 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.09742878e-02 -4.08033960e-01 -1.71863631e-01 6.41799633e-02 1.98414302e-01 1.15249131e-01 -1.70386785e-01 5.71770383e-02 -7.79476620e-03 3.84507392e-04] Err = [0.355, 8.7297447452479222] **************************************************************** Lambda = 0.356 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.10898060e-02 -4.07493604e-01 -1.71742456e-01 6.40260888e-02 1.98291120e-01 1.15316792e-01 -1.70381131e-01 5.71694232e-02 -7.79338969e-03 3.84429536e-04] Err = [0.356, 8.7297941676023996] **************************************************************** Lambda = 0.357 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.12048970e-02 -4.06955286e-01 -1.71621232e-01 6.38734523e-02 1.98168524e-01 1.15383087e-01 -1.70374784e-01 5.71616470e-02 -7.79199518e-03 3.84350895e-04] Err = [0.357, 8.7298442834727563] **************************************************************** Lambda = 0.358 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.13195164e-02 -4.06418786e-01 -1.71500043e-01 6.37215272e-02 1.98045920e-01 1.15449259e-01 -1.70368420e-01 5.71538771e-02 -7.79060229e-03 3.84272358e-04] Err = [0.358, 8.7298943349697495] **************************************************************** Lambda = 0.359 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.14336861e-02 -4.05884211e-01 -1.71378892e-01 6.35705406e-02 1.97923734e-01 1.15514585e-01 -1.70361664e-01 5.71460228e-02 -7.78920055e-03 3.84193454e-04] Err = [0.359, 8.7299447146872851] **************************************************************** Lambda = 0.36 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.15474015e-02 -4.05351489e-01 -1.71257761e-01 6.34203953e-02 1.97801728e-01 1.15579425e-01 -1.70354697e-01 5.71381269e-02 -7.78779483e-03 3.84114401e-04] Err = [0.36, 8.7299952323720742] **************************************************************** Lambda = 0.361 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.16606727e-02 -4.04820647e-01 -1.71136641e-01 6.32711699e-02 1.97680000e-01 1.15643582e-01 -1.70347412e-01 5.71301630e-02 -7.78638205e-03 3.84035058e-04] Err = [0.361, 8.7300460226580441] **************************************************************** Lambda = 0.362 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.17735113e-02 -4.04291741e-01 -1.71015544e-01 6.31229869e-02 1.97558800e-01 1.15706651e-01 -1.70339601e-01 5.71220811e-02 -7.78495643e-03 3.83955167e-04] Err = [0.362, 8.7300972859824224] **************************************************************** Lambda = 0.363 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.18858990e-02 -4.03764609e-01 -1.70894451e-01 6.29755503e-02 1.97437624e-01 1.15769484e-01 -1.70331704e-01 5.71139872e-02 -7.78353021e-03 3.83875276e-04] Err = [0.363, 8.7301485643346819] **************************************************************** Lambda = 0.364 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.19978614e-02 -4.03239406e-01 -1.70773380e-01 6.28291828e-02 1.97316991e-01 1.15831182e-01 -1.70323253e-01 5.71057685e-02 -7.78209034e-03 3.83794800e-04] Err = [0.364, 8.7302003617559656] **************************************************************** Lambda = 0.365 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.21093657e-02 -4.02715930e-01 -1.70652362e-01 6.26834433e-02 1.97196364e-01 1.15892804e-01 -1.70314816e-01 5.70975638e-02 -7.78065302e-03 3.83714470e-04] Err = [0.365, 8.7302520431636665] **************************************************************** Lambda = 0.366 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.22204312e-02 -4.02194275e-01 -1.70531394e-01 6.25385555e-02 1.97076015e-01 1.15953815e-01 -1.70306108e-01 5.70893036e-02 -7.77921016e-03 3.83633922e-04] Err = [0.366, 8.7303039408403471] **************************************************************** Lambda = 0.367 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.23310717e-02 -4.01674457e-01 -1.70410434e-01 6.23946042e-02 1.96956047e-01 1.16013984e-01 -1.70296999e-01 5.70809548e-02 -7.77775782e-03 3.83552974e-04] Err = [0.367, 8.7303561796878171] **************************************************************** Lambda = 0.368 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.24413029e-02 -4.01156508e-01 -1.70289451e-01 6.22517296e-02 1.96836536e-01 1.16073067e-01 -1.70287345e-01 5.70724812e-02 -7.77629166e-03 3.83471427e-04] Err = [0.368, 8.7304089364693311] **************************************************************** Lambda = 0.369 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.25510656e-02 -4.00640215e-01 -1.70168609e-01 6.21093041e-02 1.96716993e-01 1.16132332e-01 -1.70277866e-01 5.70640639e-02 -7.77483318e-03 3.83390266e-04] Err = [0.369, 8.7304613889866864] **************************************************************** Lambda = 0.37 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.26604241e-02 -4.00125776e-01 -1.70047744e-01 6.19679426e-02 1.96597939e-01 1.16190478e-01 -1.70267828e-01 5.70555185e-02 -7.77336052e-03 3.83308489e-04] Err = [0.37, 8.7305143755333212] **************************************************************** Lambda = 0.371 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.27693679e-02 -3.99613122e-01 -1.69926874e-01 6.18275193e-02 1.96479151e-01 1.16247899e-01 -1.70257439e-01 5.70468952e-02 -7.77187952e-03 3.83226361e-04] Err = [0.371, 8.7305676753104517] **************************************************************** Lambda = 0.372 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.28778813e-02 -3.99102194e-01 -1.69806064e-01 6.16878341e-02 1.96360612e-01 1.16304837e-01 -1.70246850e-01 5.70382341e-02 -7.77039504e-03 3.83144108e-04] Err = [0.372, 8.7306210846288064] **************************************************************** Lambda = 0.373 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.29859647e-02 -3.98592972e-01 -1.69685309e-01 6.15488732e-02 1.96242221e-01 1.16361420e-01 -1.70236124e-01 5.70295499e-02 -7.76890875e-03 3.83061803e-04] Err = [0.373, 8.7306745585051715] **************************************************************** Lambda = 0.374 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.30936182e-02 -3.98085444e-01 -1.69564627e-01 6.14106107e-02 1.96124035e-01 1.16417610e-01 -1.70225249e-01 5.70208403e-02 -7.76742044e-03 3.82979439e-04] Err = [0.374, 8.7307280915977046] **************************************************************** Lambda = 0.375 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.32008884e-02 -3.97579764e-01 -1.69443912e-01 6.12735011e-02 1.96006454e-01 1.16472443e-01 -1.70213683e-01 5.70119697e-02 -7.76591406e-03 3.82896283e-04] Err = [0.375, 8.7307823013340844] **************************************************************** Lambda = 0.376 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.33077148e-02 -3.97075696e-01 -1.69323317e-01 6.11368955e-02 1.95888910e-01 1.16527290e-01 -1.70202196e-01 5.70031305e-02 -7.76441239e-03 3.82813374e-04] Err = [0.376, 8.7308363180475812] **************************************************************** Lambda = 0.377 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.34141695e-02 -3.96573454e-01 -1.69202643e-01 6.10015014e-02 1.95771863e-01 1.16580819e-01 -1.70190019e-01 5.69941285e-02 -7.76289225e-03 3.82729650e-04] Err = [0.377, 8.7308910450850359] **************************************************************** Lambda = 0.378 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.35201701e-02 -3.96072765e-01 -1.69082141e-01 6.08664428e-02 1.95654841e-01 1.16634556e-01 -1.70178043e-01 5.69851898e-02 -7.76138068e-03 3.82646352e-04] Err = [0.378, 8.7309454015339849] **************************************************************** Lambda = 0.379 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.36257775e-02 -3.95573789e-01 -1.68961621e-01 6.07323231e-02 1.95538064e-01 1.16687565e-01 -1.70165705e-01 5.69761700e-02 -7.75986031e-03 3.82562680e-04] Err = [0.379, 8.7310001020753152] **************************************************************** Lambda = 0.38 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.37309626e-02 -3.95076430e-01 -1.68841190e-01 6.05988087e-02 1.95421460e-01 1.16740298e-01 -1.70153284e-01 5.69671412e-02 -7.75833984e-03 3.82479036e-04] Err = [0.38, 8.7310547803196368] **************************************************************** Lambda = 0.381 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.38357885e-02 -3.94580895e-01 -1.68720702e-01 6.04665407e-02 1.95305524e-01 1.16791480e-01 -1.70140059e-01 5.69579223e-02 -7.75679781e-03 3.82394438e-04] Err = [0.381, 8.7311102766122453] **************************************************************** Lambda = 0.382 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.39401807e-02 -3.94086921e-01 -1.68600356e-01 6.03347372e-02 1.95189659e-01 1.16842670e-01 -1.70126915e-01 5.69487360e-02 -7.75526065e-03 3.82310096e-04] Err = [0.382, 8.7311655611082735] **************************************************************** Lambda = 0.383 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.40441690e-02 -3.93594555e-01 -1.68480045e-01 6.02036379e-02 1.95073932e-01 1.16893495e-01 -1.70113620e-01 5.69395219e-02 -7.75372103e-03 3.82225669e-04] Err = [0.383, 8.7312209339071671] **************************************************************** Lambda = 0.384 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.41477522e-02 -3.93103806e-01 -1.68359809e-01 6.00732295e-02 1.94958463e-01 1.16943846e-01 -1.70100131e-01 5.69302710e-02 -7.75217801e-03 3.82141120e-04] Err = [0.384, 8.7312764072887834] **************************************************************** Lambda = 0.385 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.42509804e-02 -3.92614816e-01 -1.68239515e-01 5.99440006e-02 1.94843557e-01 1.16992823e-01 -1.70085928e-01 5.69208515e-02 -7.75061590e-03 3.82055728e-04] Err = [0.385, 8.7313326123978801] **************************************************************** Lambda = 0.386 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.43537700e-02 -3.92127292e-01 -1.68119385e-01 5.98150671e-02 1.94728566e-01 1.17042153e-01 -1.70071993e-01 5.69115109e-02 -7.74906407e-03 3.81970836e-04] Err = [0.386, 8.7313883917101265] **************************************************************** Lambda = 0.387 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.44561753e-02 -3.91641402e-01 -1.67999285e-01 5.96869611e-02 1.94613897e-01 1.17090772e-01 -1.70057723e-01 5.69020973e-02 -7.74750451e-03 3.81885621e-04] Err = [0.387, 8.7314444577379557] **************************************************************** Lambda = 0.388 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.45582136e-02 -3.91157169e-01 -1.67879165e-01 5.95598218e-02 1.94499615e-01 1.17138436e-01 -1.70042972e-01 5.68925729e-02 -7.74593263e-03 3.81799872e-04] Err = [0.388, 8.7315009768821987] **************************************************************** Lambda = 0.389 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.46598516e-02 -3.90674520e-01 -1.67759163e-01 5.94333233e-02 1.94385653e-01 1.17185617e-01 -1.70028035e-01 5.68830151e-02 -7.74435789e-03 3.81714027e-04] Err = [0.389, 8.7315575893823354] **************************************************************** Lambda = 0.39 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.47610958e-02 -3.90193394e-01 -1.67639201e-01 5.93074606e-02 1.94271750e-01 1.17232577e-01 -1.70013021e-01 5.68734471e-02 -7.74278269e-03 3.81628186e-04] Err = [0.39, 8.7316142040977258] **************************************************************** Lambda = 0.391 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.48619712e-02 -3.89713904e-01 -1.67519270e-01 5.91824901e-02 1.94158318e-01 1.17278575e-01 -1.69997540e-01 5.68637739e-02 -7.74119599e-03 3.81541852e-04] Err = [0.391, 8.7316712301227071] **************************************************************** Lambda = 0.392 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.49624463e-02 -3.89235905e-01 -1.67399425e-01 5.90580713e-02 1.94044901e-01 1.17324509e-01 -1.69982077e-01 5.68541148e-02 -7.73961178e-03 3.81455659e-04] Err = [0.392, 8.731728156014146] **************************************************************** Lambda = 0.393 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.50625612e-02 -3.88759536e-01 -1.67279598e-01 5.89345675e-02 1.93932010e-01 1.17369381e-01 -1.69966092e-01 5.68443370e-02 -7.73801446e-03 3.81368899e-04] Err = [0.393, 8.7317855572962078] **************************************************************** Lambda = 0.394 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.51622738e-02 -3.88284622e-01 -1.67159869e-01 5.88115435e-02 1.93819092e-01 1.17414310e-01 -1.69950192e-01 5.68345904e-02 -7.73642166e-03 3.81282373e-04] Err = [0.394, 8.7318427784795229] **************************************************************** Lambda = 0.395 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.52615950e-02 -3.87811209e-01 -1.67040251e-01 5.86890913e-02 1.93706401e-01 1.17458906e-01 -1.69934182e-01 5.68248277e-02 -7.73482792e-03 3.81195835e-04] Err = [0.395, 8.7318999972231008] **************************************************************** Lambda = 0.396 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.53605878e-02 -3.87339468e-01 -1.66920565e-01 5.85678047e-02 1.93594315e-01 1.17502055e-01 -1.69917414e-01 5.68148853e-02 -7.73321371e-03 3.81108390e-04] Err = [0.396, 8.7319579944427179] **************************************************************** Lambda = 0.397 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.54591670e-02 -3.86869116e-01 -1.66801040e-01 5.84468214e-02 1.93482154e-01 1.17545512e-01 -1.69900886e-01 5.68050138e-02 -7.73160879e-03 3.81021398e-04] Err = [0.397, 8.7320156130434636] **************************************************************** Lambda = 0.398 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.55573802e-02 -3.86400308e-01 -1.66681576e-01 5.83266099e-02 1.93370353e-01 1.17588259e-01 -1.69884029e-01 5.67950713e-02 -7.72999640e-03 3.80934096e-04] Err = [0.398, 8.7320735038014359] **************************************************************** Lambda = 0.399 feature_names= ['1', 'x0', 'x0^2', 'x0^3', 'x0^4', 'x0^5', 'x0^6', 'x0^7', 'x0^8', 'x0^9'] coef= [ -9.56552185e-02 -3.85932966e-01 -1.66562166e-01 5.82070154e-02 1.93258711e-01 1.17630666e-01 -1.69867037e-01 5.67851048e-02 -7.72838197e-03 3.80846728e-04] Err = [0.399, 8.7321314370478138] **************************************************************** min_e = [0.258, 8.726875114433275]
In [89]:
plt.plot(L, np.log(E_T) , 'b-')
plt.title('$Lambda \ vs. Error, blue:E(w)=E_D+E_W$')
plt.xlabel('lambda')
plt.ylabel('log( E(w) )')
Out[89]:
<matplotlib.text.Text at 0x1205d2e8>
In [88]:
Err = pd.DataFrame({'lambda':L,
'log(E)':np.log(E_T)})
Err
Out[88]:
| lambda | log(E) | |
|---|---|---|
| 0 | 0.200 | 2.166627 |
| 1 | 0.201 | 2.166618 |
| 2 | 0.202 | 2.166610 |
| 3 | 0.203 | 2.166602 |
| 4 | 0.204 | 2.166594 |
| 5 | 0.205 | 2.166586 |
| 6 | 0.206 | 2.166579 |
| 7 | 0.207 | 2.166571 |
| 8 | 0.208 | 2.166564 |
| 9 | 0.209 | 2.166557 |
| 10 | 0.210 | 2.166551 |
| 11 | 0.211 | 2.166544 |
| 12 | 0.212 | 2.166538 |
| 13 | 0.213 | 2.166531 |
| 14 | 0.214 | 2.166525 |
| 15 | 0.215 | 2.166520 |
| 16 | 0.216 | 2.166514 |
| 17 | 0.217 | 2.166509 |
| 18 | 0.218 | 2.166503 |
| 19 | 0.219 | 2.166498 |
| 20 | 0.220 | 2.166493 |
| 21 | 0.221 | 2.166488 |
| 22 | 0.222 | 2.166484 |
| 23 | 0.223 | 2.166479 |
| 24 | 0.224 | 2.166475 |
| 25 | 0.225 | 2.166471 |
| 26 | 0.226 | 2.166466 |
| 27 | 0.227 | 2.166463 |
| 28 | 0.228 | 2.166459 |
| 29 | 0.229 | 2.166455 |
| ... | ... | ... |
| 170 | 0.370 | 2.166824 |
| 171 | 0.371 | 2.166830 |
| 172 | 0.372 | 2.166837 |
| 173 | 0.373 | 2.166843 |
| 174 | 0.374 | 2.166849 |
| 175 | 0.375 | 2.166855 |
| 176 | 0.376 | 2.166861 |
| 177 | 0.377 | 2.166867 |
| 178 | 0.378 | 2.166874 |
| 179 | 0.379 | 2.166880 |
| 180 | 0.380 | 2.166886 |
| 181 | 0.381 | 2.166893 |
| 182 | 0.382 | 2.166899 |
| 183 | 0.383 | 2.166905 |
| 184 | 0.384 | 2.166912 |
| 185 | 0.385 | 2.166918 |
| 186 | 0.386 | 2.166924 |
| 187 | 0.387 | 2.166931 |
| 188 | 0.388 | 2.166937 |
| 189 | 0.389 | 2.166944 |
| 190 | 0.390 | 2.166950 |
| 191 | 0.391 | 2.166957 |
| 192 | 0.392 | 2.166963 |
| 193 | 0.393 | 2.166970 |
| 194 | 0.394 | 2.166976 |
| 195 | 0.395 | 2.166983 |
| 196 | 0.396 | 2.166990 |
| 197 | 0.397 | 2.166996 |
| 198 | 0.398 | 2.167003 |
| 199 | 0.399 | 2.167009 |
200 rows × 2 columns
In [ ]:
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