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GaelVaroquaux/sklearn_EN_example.py

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Created September 29, 2012 16:16
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Demonstrate that ElasticNet doesn't fit all the way, even for rather strict convergence criteria
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sklearn_EN_example.py
import numpy as np
import sklearn.linear_model as lm
X = np.array([[ -2.18252949e-01, -8.21949578e-02, -4.64055457e-02,
-1.78405908e-01, -1.93863740e-01, 5.30667625e-02,
1.83851107e-01, 1.23426449e-01, 1.97396315e-01,
-2.12615837e-01, 7.06452283e-02, -1.94509405e-01,
-9.77929516e-02, 2.07135018e-01, -3.40368338e-02,
2.02970673e-01, -2.28669466e-01, 4.17398420e-02,
1.80163132e-01, 3.24254938e-02, -2.41198452e-03,
-7.45212064e-03, -1.74771571e-01, -3.97269909e-03,
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1.05013626e-01, -1.10075629e-01, 1.87287470e-01,
2.49763135e-02, -2.16111837e-01, -6.47202419e-02,
2.01951109e-01, 1.07978359e-01, -8.05947873e-02,
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3.55754078e-02, 8.22767462e-02, 2.05296709e-01,
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1.30167216e-01, 7.76274455e-02, 1.63927079e-01,
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1.28615805e-01, 1.21000402e-01, 1.99705032e-01,
1.34049181e-01, -1.53081953e-01, -1.40380331e-01,
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6.61147761e-02, 3.46967326e-02, -1.59629784e-01,
-7.82494527e-03, -3.50305111e-03, 2.04735603e-01],
[ -2.35790250e-02, 1.70550727e-01, 7.22324969e-03,
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1.38956733e-01, 9.31597480e-02, -1.66696408e-01,
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1.95599991e-01, -2.15772038e-01, 2.02210007e-01,
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8.58230716e-02, 9.81542854e-02, -1.04827838e-01],
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5.70017057e-02, -1.70799334e-01, 1.91850201e-01,
1.17949766e-01, -7.92771444e-02, -1.74352499e-01,
-1.00057423e-01, 2.06836661e-01, 1.32038001e-01,
-2.27197438e-01, -6.56188077e-02, 1.50160134e-01,
3.97729763e-02, -2.14510805e-01, -2.82669536e-02,
-2.13846896e-01, 2.04227002e-01, -1.35633411e-01,
-1.94029350e-01, -2.01664908e-01, 8.07306250e-02,
2.05156814e-01, 1.26442873e-01, 6.63365786e-02,
8.90379793e-02, -1.86538822e-01, 4.40779724e-02,
-4.91958237e-02, -1.57908247e-01, -1.68275026e-01,
-1.03929482e-01, -1.73372598e-01, 1.97283748e-01,
-8.31875181e-03, -8.06629460e-02, 1.73957140e-01,
-1.91820270e-01, -3.35885428e-02, 5.63264577e-02,
2.41252331e-02, -7.99569714e-02, -1.66138428e-01,
-5.73439661e-02, 1.04155535e-02, -1.21692216e-01,
1.91541933e-01, 1.80653366e-01, 6.89551444e-02,
-2.28602386e-01, 8.15565497e-03, 2.06510153e-01],
[ -4.25901641e-02, 2.34394814e-04, 9.76419075e-02,
1.53523022e-01, 1.96170737e-01, -2.29841608e-01,
-1.72856422e-01, -1.24728907e-01, -2.00310216e-01,
1.68629623e-01, -1.32964459e-01, -6.78350785e-02,
1.28424230e-01, -3.03423108e-02, 2.01618616e-01,
9.86424746e-03, 1.21013061e-01, 8.35368296e-03,
1.54946345e-01, 1.82819084e-01, -1.06411917e-01,
-1.63195098e-01, 1.74532852e-01, -8.81864713e-02,
6.40897761e-02, 1.26096448e-01, -1.90758161e-01,
-2.10600454e-01, -1.55578973e-01, 7.07860492e-02,
5.41833709e-02, -5.44805243e-02, -1.10292807e-01,
6.34005082e-03, 1.07928886e-01, 2.04097836e-01,
-8.66707300e-02, 2.02245614e-01, -2.15229129e-01,
-1.53844708e-01, 2.00996915e-01, -2.13904044e-01,
-2.22512377e-01, 1.92875867e-01, -1.47948003e-02,
-5.04757064e-02, -1.43995947e-01, -2.09245974e-01,
1.41476379e-01, -1.21918118e-01, -1.77709746e-01,
7.78043328e-02, -1.39558460e-01, -1.73917851e-01,
1.25440865e-01, 1.92912166e-01, 2.08052976e-01,
1.86750986e-01, 2.08460468e-01, 1.98229419e-01,
5.01816257e-02, -2.25697970e-01, 1.94222443e-01,
-8.56228947e-02, 1.48773224e-01, -6.16983719e-02,
1.56671053e-01, -1.88641652e-01, 1.78155657e-01,
-1.81847499e-01, -1.61222723e-02, -1.36297864e-01,
4.57828320e-02, -1.86515620e-01, 1.74165053e-01,
-1.98453052e-01, -1.29635302e-01, -1.63674304e-02,
-1.87121665e-02, 1.31750279e-02, 6.04380471e-04,
1.98790239e-01, -2.30909138e-01, -8.97866133e-02,
1.35617363e-01, -1.11993119e-01, -1.36684265e-01,
-1.03718282e-01, -8.87212786e-02, 4.65147143e-02,
-1.96743530e-01, 1.76685305e-01, 1.07783881e-01,
-1.88660533e-01, -2.05733191e-01, -8.51838157e-02,
2.05021402e-01, 1.19573529e-01, 1.80278166e-01,
-4.17877904e-02, -1.71459629e-01, -1.86489446e-01,
-2.25062486e-01, 1.15386174e-01, -8.64484070e-02,
2.06709331e-01, 2.07010546e-01, -1.27109942e-01,
1.78432983e-02, -2.19896743e-01, 7.48802191e-02,
3.35977199e-02, -1.24938034e-01, 1.66078582e-01,
-1.37575671e-02, -1.13667236e-02, 1.49888021e-01,
-1.59031883e-01, 8.35903572e-02, 7.55671473e-02,
3.95562757e-03, 1.97323004e-01, -1.74210640e-01,
-2.23966072e-01, 1.59213422e-01, 6.11683262e-02,
4.49523757e-02, 6.60514918e-02, 1.96301924e-01,
1.05147595e-01, -1.73719036e-01, -1.02367955e-01,
1.59218253e-01, -6.70004817e-02, 9.78234863e-02,
2.08227359e-01, 1.44398005e-01, 2.04797875e-01,
6.18140134e-02, -2.17109757e-01, 2.08353168e-01,
-2.11232667e-01, 2.04553091e-01, 1.95062940e-01,
1.55559550e-01, -6.33761484e-02, -2.01846189e-01,
1.20340756e-02, -1.32144027e-02, 1.46370531e-01],
[ 1.70915760e-01, 2.03546100e-01, -1.16222328e-01,
1.54953577e-01, 7.62485883e-02, 8.09962332e-02,
-1.02384822e-01, 1.95604318e-01, 1.77673519e-01,
9.03014209e-02, 1.86091055e-01, 2.07707589e-01,
9.12203033e-02, -2.19164378e-02, -1.52579882e-01,
-2.27979169e-01, 1.90984663e-01, -1.48202210e-01,
-2.20990466e-01, -1.81793412e-01, 9.41186084e-02,
1.76202714e-01, 8.21186732e-02, 9.06789601e-02,
-5.54574372e-02, 4.33614452e-02, -8.30432934e-02,
2.07995916e-01, 2.09862146e-01, 2.09173039e-01,
-1.72494476e-01, -9.30008036e-02, -1.88809980e-01,
8.05774211e-02, 1.96845931e-03, -2.69613376e-02,
-2.14101626e-01, -8.86287555e-02, -8.42054774e-02,
-1.79571356e-01, 1.77857623e-01, 1.51922057e-02,
6.17435586e-02, -1.55287524e-01, 1.43757872e-01,
1.13646181e-01, 1.18717742e-01, 1.76444363e-01,
-2.27053812e-01, -1.68986713e-01, -1.67221071e-01,
1.49518771e-01, 2.11075695e-01, 2.05026432e-01,
1.22836756e-01, -1.59390851e-01, -2.02273777e-01,
3.42225167e-02, 1.02117174e-01, -2.16723685e-01,
9.87815042e-02, 3.63332994e-03, 1.80832110e-01,
6.66649483e-02, -8.99107358e-02, 2.11571143e-02,
-1.80023809e-01, 1.99790049e-01, 6.93567262e-02,
1.27490820e-01, 1.91296401e-01, 2.28243282e-02,
-1.94471829e-01, 5.21854629e-02, -6.41543251e-02,
2.05489634e-01, -2.03119097e-01, -4.02862550e-02,
-2.10886942e-01, 4.67159818e-02, -2.22843625e-01,
2.05377825e-01, 3.80569695e-02, -1.76928186e-01,
-1.49460475e-01, -6.49410790e-02, 1.85035852e-01,
1.82264261e-03, -2.17420636e-01, 4.46257355e-03,
1.84088620e-01, 1.84151447e-01, -6.99089273e-02,
5.76948502e-02, 3.54084276e-02, 1.76499994e-01,
-2.00134293e-01, -1.42296516e-01, -2.00948734e-01,
1.78291748e-01, -9.66054777e-02, 2.00045816e-01,
1.52593082e-01, 1.03128940e-01, -1.52206811e-01,
1.64128157e-02, -2.06911233e-01, 1.72539082e-01,
5.16986638e-02, -6.66435659e-02, -8.55202455e-02,
-1.55333477e-02, 1.99124799e-02, -6.04965558e-02,
-6.61728108e-02, -4.90998600e-02, 1.93879877e-01,
1.57728578e-01, 1.98579846e-01, -2.29169295e-01,
-2.09050364e-01, -1.60905608e-01, -1.78532159e-01,
1.74561086e-01, -7.91594964e-02, -5.62419478e-02,
-2.16618536e-01, -1.67170722e-01, 1.39804169e-01,
2.06488790e-01, -8.64094304e-02, 1.05901063e-01,
-7.90331423e-02, 1.12827102e-01, -1.25494931e-01,
2.05782917e-01, -2.09026551e-01, -1.76270688e-01,
-4.63541931e-02, 1.66058135e-01, -2.08367306e-02,
-1.10093556e-01, -1.02651631e-01, -1.40700523e-01,
-1.64853965e-01, -1.27759653e-01, -1.37820588e-01,
1.09231017e-01, 1.97140760e-01, -2.18872756e-01]]).T
y = np.array([ -1.49887702e-01, -2.73141605e-01, -8.74390578e-02,
-2.28770200e-01, -1.92615722e-01, 2.79035881e-01,
6.21090112e-02, -8.08655163e-02, 2.43111476e-02,
-1.38384004e-01, -1.64678170e-01, -1.54817858e-01,
-2.59994522e-01, 1.82076144e-01, 2.94713777e-03,
2.59315256e-01, -2.61637907e-01, -1.00586141e-01,
1.06480416e-01, -4.30676527e-02, 2.00153383e-01,
2.44524788e-01, -2.43560668e-01, -1.81112024e-01,
-3.39632977e-04, -1.95902492e-01, 4.73185429e-02,
2.51098329e-01, 1.14697343e-01, -1.51531087e-01,
1.60942208e-02, -1.18433306e-02, 9.52067927e-03,
-1.07159682e-01, -1.41670775e-01, -1.13733224e-01,
2.10013695e-01, -1.87685566e-01, 1.78789373e-01,
1.68929061e-01, -1.26880307e-01, 2.16587236e-01,
8.67597918e-02, 9.33333333e-02, -1.44957546e-01,
2.75979184e-02, 2.06726924e-01, 1.88649685e-01,
2.14943851e-01, -8.55655985e-03, 3.49701452e-01,
-3.04365927e-01, 2.75979184e-02, 2.36307861e-01,
-1.41670775e-01, 3.58148452e-02, 2.24804163e-01,
-1.36740619e-01, -2.23840044e-01, 2.31377705e-01,
-1.33453848e-01, 1.82076144e-01, -1.51531087e-01,
7.52560942e-02, -8.41522870e-02, 1.37704738e-01,
-6.11448918e-02, 8.84031772e-02, -1.69608326e-01,
3.41714599e-02, -9.07258285e-02, -8.41522870e-02,
2.59545330e-02, -1.07159682e-01, -6.93618187e-02,
2.49454944e-01, 1.59068748e-01, 1.26201041e-01,
1.57425363e-01, -1.12089838e-01, 7.68994796e-02,
-1.79468639e-01, 3.46414681e-01, 9.00465626e-02,
1.52495207e-01, -1.48244317e-01, -8.41522870e-02,
-1.21950151e-01, 1.57425363e-01, -1.23593536e-01,
-3.62640373e-03, -1.56461243e-01, -1.38384004e-01,
-1.26880307e-01, 1.52495207e-01, -1.49887702e-01,
1.49208436e-01, 1.77145987e-01, 1.90293070e-01,
-1.66321556e-01, 1.82076144e-01, 6.04656259e-02,
2.59315256e-01, -2.20553273e-01, 6.37523966e-02,
-1.99189263e-01, 1.73859217e-01, -8.41522870e-02,
-1.71251712e-01, 2.98756505e-01, 1.04837031e-01,
-8.57956724e-02, -1.03872912e-01, -1.10446453e-01,
-2.17036428e-02, 1.96866612e-01, -2.45204054e-01,
-7.59353602e-02, -1.61391400e-01, 2.01796768e-01,
-6.60750479e-02, -8.55655985e-03, 1.22914270e-01,
2.06726924e-01, -1.56461243e-01, -1.98301835e-03,
1.55781978e-01, -4.96411942e-02, -2.41917283e-01,
-1.86042180e-01, 6.86825527e-02, 4.89619282e-02,
-9.72993700e-02, -6.44316626e-02, 1.21270885e-01,
-2.02476034e-01, 1.54138592e-01, 1.22914270e-01,
-2.17036428e-02, 2.41238017e-01, -2.04119419e-01,
2.03440153e-01, -1.59748014e-01, -9.23692139e-02,
2.08370310e-01, -1.31810463e-01, 1.44278280e-01,
-1.99189263e-01, -1.99189263e-01, 1.60942208e-02])
alpha = 0
rho = 0
solver_params = dict(alpha=alpha,
rho=rho,
fit_intercept=False,
positive=False,
tol=1e-64,
max_iter=100000)
enet = lm.ElasticNet(**solver_params)
enet.fit(X,y)
y_hat = np.dot(X, enet.coef_)
print("With ElasticNet: %1.4f"%np.corrcoef(y,y_hat)[0,1])
for i in range(10):
enet.warm_start = True
enet.fit(X,y)
y_hat = np.dot(X, enet.coef_)
print("With ElasticNet (%i refit): %1.4f" % (i + 1,
np.corrcoef(y,y_hat)[0,1]))
ols = lm.LinearRegression(fit_intercept=False)
ols.fit(X,y)
y_hat_ols = np.dot(X, ols.coef_)
print("With LinearRegression: %1.4f"%np.corrcoef(y, y_hat_ols)[0,1])
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