sklearn.linear_model.ridge 中的统计摘要 table？
statistical summary table in sklearn.linear_model.ridge?
在 OLS 形式的 StatsModels 中，results.summary 显示回归结果的摘要（例如 AIC、BIC、R 平方...）
有什么方法可以在 sklearn.linear_model.ridge 中获得此摘要 table？
如果有人能指导我，我将不胜感激。谢谢。
据我所知，sklearn 中没有类似 R（或 Statsmodels）的摘要 table。 （请勾选this answer）
相反，如果您需要它，statsmodels.regression.linear_model.OLS.fit_regularized class。 （L1_wt=0 用于岭回归。）
目前看来，model.fit_regularized(~).summary() returns None 尽管有下面的文档字符串。但是对象有params，summary()不知何故可以使用。
Returns: A RegressionResults object, of the same type returned by fit.
示例。
示例数据不适用于岭回归，但无论如何我都会尝试。
在.
import numpy as np
import pandas as pd
import statsmodels
import statsmodels.api as sm
import matplotlib.pyplot as plt
statsmodels.__version__
出局。
'0.8.0rc1'
在.
data = sm.datasets.ccard.load()
print "endog: " + data.endog_name
print "exog: " + ', '.join(data.exog_name)
data.exog[:5, :]
出局。
endog: AVGEXP
exog: AGE, INCOME, INCOMESQ, OWNRENT
Out[2]:
array([[ 38. , 4.52 , 20.4304, 1. ],
[ 33. , 2.42 , 5.8564, 0. ],
[ 34. , 4.5 , 20.25 , 1. ],
[ 31. , 2.54 , 6.4516, 0. ],
[ 32. , 9.79 , 95.8441, 1. ]])
在.
y, X = data.endog, data.exog
model = sm.OLS(y, X)
results_fu = model.fit()
print results_fu.summary()
出局。
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.543
Model: OLS Adj. R-squared: 0.516
Method: Least Squares F-statistic: 20.22
Date: Wed, 19 Oct 2016 Prob (F-statistic): 5.24e-11
Time: 17:22:48 Log-Likelihood: -507.24
No. Observations: 72 AIC: 1022.
Df Residuals: 68 BIC: 1032.
Df Model: 4
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
x1 -6.8112 4.551 -1.497 0.139 -15.892 2.270
x2 175.8245 63.743 2.758 0.007 48.628 303.021
x3 -9.7235 6.030 -1.613 0.111 -21.756 2.309
x4 54.7496 80.044 0.684 0.496 -104.977 214.476
==============================================================================
Omnibus: 76.325 Durbin-Watson: 1.692
Prob(Omnibus): 0.000 Jarque-Bera (JB): 649.447
Skew: 3.194 Prob(JB): 9.42e-142
Kurtosis: 16.255 Cond. No. 87.5
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
在.
frames = []
for n in np.arange(0, 0.25, 0.05).tolist():
results_fr = model.fit_regularized(L1_wt=0, alpha=n, start_params=results_fu.params)
results_fr_fit = sm.regression.linear_model.OLSResults(model,
results_fr.params,
model.normalized_cov_params)
frames.append(np.append(results_fr.params, results_fr_fit.ssr))
df = pd.DataFrame(frames, columns=data.exog_name + ['ssr*'])
df.index=np.arange(0, 0.25, 0.05).tolist()
df.index.name = 'alpha*'
df.T
出局。
在.
%matplotlib inline
fig, ax = plt.subplots(1, 2, figsize=(14, 4))
ax[0] = df.iloc[:, :-1].plot(ax=ax[0])
ax[0].set_title('Coefficient')
ax[1] = df.iloc[:, -1].plot(ax=ax[1])
ax[1].set_title('SSR')
出局。
在.
results_fr = model.fit_regularized(L1_wt=0, alpha=0.04, start_params=results_fu.params)
final = sm.regression.linear_model.OLSResults(model,
results_fr.params,
model.normalized_cov_params)
print final.summary()
出局。
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.543
Model: OLS Adj. R-squared: 0.516
Method: Least Squares F-statistic: 20.17
Date: Wed, 19 Oct 2016 Prob (F-statistic): 5.46e-11
Time: 17:22:49 Log-Likelihood: -507.28
No. Observations: 72 AIC: 1023.
Df Residuals: 68 BIC: 1032.
Df Model: 4
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
x1 -5.6375 4.554 -1.238 0.220 -14.724 3.449
x2 159.1412 63.781 2.495 0.015 31.867 286.415
x3 -8.1360 6.034 -1.348 0.182 -20.176 3.904
x4 44.2597 80.093 0.553 0.582 -115.564 204.083
==============================================================================
Omnibus: 76.819 Durbin-Watson: 1.694
Prob(Omnibus): 0.000 Jarque-Bera (JB): 658.948
Skew: 3.220 Prob(JB): 8.15e-144
Kurtosis: 16.348 Cond. No. 87.5
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
from statsmodels.tools.tools import pinv_extended
X_train = sm.add_constant(X_train)
model = sm.OLS(y_train, X_train)
# If True, the model is refit using only the variables that have non-zero
# coefficients in the regularized fit. The refitted model is not regularized.
result = model.fit_regularized(
method = 'elastic_net',
alpha = alp,
L1_wt = l1,
start_params = None,
profile_scale = False,
#refit = True,
refit = False,
maxiter = 9000,
zero_tol = 1e-5,
)
pinv_wexog,_ = pinv_extended(model.wexog)
normalized_cov_params = np.dot(pinv_wexog, np.transpose(pinv_wexog))
final = sm.regression.linear_model.OLSResults(model,
result.params,
normalized_cov_params)
#print(final.summary())
x = sm.add_constant(X_test)
#x = X_test
R2 = r2_score(y_test, final.predict(x))
p = final.pvalues
t = final.tvalues
感谢@Bugee，我创建了以下函数，returns statsmodels 指标，例如 rsquared 和 rsquared_adj，以及 summary()。
您也可以使用 sklearn 线性模型（LinearRegression、Lasso、Ridge...）和 statsmodels OLS 以及正则化 OLS。
from statsmodels.tools.tools import pinv_extended
import statsmodels.api as sm
import sklearn, statsmodels
def regression_analysis(X, y, model):
is_statsmodels = False
is_sklearn = False
# check for accepted linear models
if type(model) in [sklearn.linear_model._base.LinearRegression,
sklearn.linear_model._ridge.Ridge,
sklearn.linear_model._ridge.RidgeCV,
sklearn.linear_model._coordinate_descent.Lasso,
sklearn.linear_model._coordinate_descent.LassoCV,
sklearn.linear_model._coordinate_descent.ElasticNet,
sklearn.linear_model._coordinate_descent.ElasticNetCV,
]:
is_sklearn = True
elif type(model) in [statsmodels.regression.linear_model.OLS,
statsmodels.base.elastic_net.RegularizedResults,
]:
is_statsmodels = True
else:
print("Only linear models are supported!")
return None
has_intercept = False
if is_statsmodels and all(np.array(X)[:,0]==1):
# statsmodels add_constant has been used already
has_intercept = True
elif is_sklearn and model.intercept_:
has_intercept = True
if is_statsmodels:
# add_constant has been used already
x = X
model_params = model.params
else: # sklearn model
if has_intercept:
x = sm.add_constant(X)
model_params = np.hstack([np.array([model.intercept_]), model.coef_])
else:
x = X
model_params = model.coef_
#y = np.array(y).ravel()
# define the OLS model
olsModel = sm.OLS(y, x)
pinv_wexog,_ = pinv_extended(x)
normalized_cov_params = np.dot(pinv_wexog, np.transpose(pinv_wexog))
return sm.regression.linear_model.OLSResults(olsModel, model_params, normalized_cov_params)
如何使用？
from sklearn.linear_model import Ridge
skridge = Ridge(alpha=0.2, max_iter=9000, tol=1e-5, fit_intercept=True)
skridge.fit(X,y)
result = regression_analysis(X, y, skridge)
result.summary()
在 OLS 形式的 StatsModels 中，results.summary 显示回归结果的摘要（例如 AIC、BIC、R 平方...）
有什么方法可以在 sklearn.linear_model.ridge 中获得此摘要 table？
如果有人能指导我，我将不胜感激。谢谢。
据我所知，sklearn 中没有类似 R（或 Statsmodels）的摘要 table。 （请勾选this answer）
相反，如果您需要它，statsmodels.regression.linear_model.OLS.fit_regularized class。 （L1_wt=0 用于岭回归。）
目前看来，model.fit_regularized(~).summary() returns None 尽管有下面的文档字符串。但是对象有params，summary()不知何故可以使用。
Returns: A RegressionResults object, of the same type returned by
fit.
示例。
示例数据不适用于岭回归，但无论如何我都会尝试。
在.
import numpy as np
import pandas as pd
import statsmodels
import statsmodels.api as sm
import matplotlib.pyplot as plt
statsmodels.__version__
出局。
'0.8.0rc1'
在.
data = sm.datasets.ccard.load()
print "endog: " + data.endog_name
print "exog: " + ', '.join(data.exog_name)
data.exog[:5, :]
出局。
endog: AVGEXP
exog: AGE, INCOME, INCOMESQ, OWNRENT
Out[2]:
array([[ 38. , 4.52 , 20.4304, 1. ],
[ 33. , 2.42 , 5.8564, 0. ],
[ 34. , 4.5 , 20.25 , 1. ],
[ 31. , 2.54 , 6.4516, 0. ],
[ 32. , 9.79 , 95.8441, 1. ]])
在.
y, X = data.endog, data.exog
model = sm.OLS(y, X)
results_fu = model.fit()
print results_fu.summary()
出局。
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.543
Model: OLS Adj. R-squared: 0.516
Method: Least Squares F-statistic: 20.22
Date: Wed, 19 Oct 2016 Prob (F-statistic): 5.24e-11
Time: 17:22:48 Log-Likelihood: -507.24
No. Observations: 72 AIC: 1022.
Df Residuals: 68 BIC: 1032.
Df Model: 4
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
x1 -6.8112 4.551 -1.497 0.139 -15.892 2.270
x2 175.8245 63.743 2.758 0.007 48.628 303.021
x3 -9.7235 6.030 -1.613 0.111 -21.756 2.309
x4 54.7496 80.044 0.684 0.496 -104.977 214.476
==============================================================================
Omnibus: 76.325 Durbin-Watson: 1.692
Prob(Omnibus): 0.000 Jarque-Bera (JB): 649.447
Skew: 3.194 Prob(JB): 9.42e-142
Kurtosis: 16.255 Cond. No. 87.5
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
在.
frames = []
for n in np.arange(0, 0.25, 0.05).tolist():
results_fr = model.fit_regularized(L1_wt=0, alpha=n, start_params=results_fu.params)
results_fr_fit = sm.regression.linear_model.OLSResults(model,
results_fr.params,
model.normalized_cov_params)
frames.append(np.append(results_fr.params, results_fr_fit.ssr))
df = pd.DataFrame(frames, columns=data.exog_name + ['ssr*'])
df.index=np.arange(0, 0.25, 0.05).tolist()
df.index.name = 'alpha*'
df.T
出局。
在.
%matplotlib inline
fig, ax = plt.subplots(1, 2, figsize=(14, 4))
ax[0] = df.iloc[:, :-1].plot(ax=ax[0])
ax[0].set_title('Coefficient')
ax[1] = df.iloc[:, -1].plot(ax=ax[1])
ax[1].set_title('SSR')
出局。
在.
results_fr = model.fit_regularized(L1_wt=0, alpha=0.04, start_params=results_fu.params)
final = sm.regression.linear_model.OLSResults(model,
results_fr.params,
model.normalized_cov_params)
print final.summary()
出局。
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.543
Model: OLS Adj. R-squared: 0.516
Method: Least Squares F-statistic: 20.17
Date: Wed, 19 Oct 2016 Prob (F-statistic): 5.46e-11
Time: 17:22:49 Log-Likelihood: -507.28
No. Observations: 72 AIC: 1023.
Df Residuals: 68 BIC: 1032.
Df Model: 4
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
x1 -5.6375 4.554 -1.238 0.220 -14.724 3.449
x2 159.1412 63.781 2.495 0.015 31.867 286.415
x3 -8.1360 6.034 -1.348 0.182 -20.176 3.904
x4 44.2597 80.093 0.553 0.582 -115.564 204.083
==============================================================================
Omnibus: 76.819 Durbin-Watson: 1.694
Prob(Omnibus): 0.000 Jarque-Bera (JB): 658.948
Skew: 3.220 Prob(JB): 8.15e-144
Kurtosis: 16.348 Cond. No. 87.5
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
from statsmodels.tools.tools import pinv_extended
X_train = sm.add_constant(X_train)
model = sm.OLS(y_train, X_train)
# If True, the model is refit using only the variables that have non-zero
# coefficients in the regularized fit. The refitted model is not regularized.
result = model.fit_regularized(
method = 'elastic_net',
alpha = alp,
L1_wt = l1,
start_params = None,
profile_scale = False,
#refit = True,
refit = False,
maxiter = 9000,
zero_tol = 1e-5,
)
pinv_wexog,_ = pinv_extended(model.wexog)
normalized_cov_params = np.dot(pinv_wexog, np.transpose(pinv_wexog))
final = sm.regression.linear_model.OLSResults(model,
result.params,
normalized_cov_params)
#print(final.summary())
x = sm.add_constant(X_test)
#x = X_test
R2 = r2_score(y_test, final.predict(x))
p = final.pvalues
t = final.tvalues
感谢@Bugee，我创建了以下函数，returns statsmodels 指标，例如 rsquared 和 rsquared_adj，以及 summary()。
您也可以使用 sklearn 线性模型（LinearRegression、Lasso、Ridge...）和 statsmodels OLS 以及正则化 OLS。
from statsmodels.tools.tools import pinv_extended
import statsmodels.api as sm
import sklearn, statsmodels
def regression_analysis(X, y, model):
is_statsmodels = False
is_sklearn = False
# check for accepted linear models
if type(model) in [sklearn.linear_model._base.LinearRegression,
sklearn.linear_model._ridge.Ridge,
sklearn.linear_model._ridge.RidgeCV,
sklearn.linear_model._coordinate_descent.Lasso,
sklearn.linear_model._coordinate_descent.LassoCV,
sklearn.linear_model._coordinate_descent.ElasticNet,
sklearn.linear_model._coordinate_descent.ElasticNetCV,
]:
is_sklearn = True
elif type(model) in [statsmodels.regression.linear_model.OLS,
statsmodels.base.elastic_net.RegularizedResults,
]:
is_statsmodels = True
else:
print("Only linear models are supported!")
return None
has_intercept = False
if is_statsmodels and all(np.array(X)[:,0]==1):
# statsmodels add_constant has been used already
has_intercept = True
elif is_sklearn and model.intercept_:
has_intercept = True
if is_statsmodels:
# add_constant has been used already
x = X
model_params = model.params
else: # sklearn model
if has_intercept:
x = sm.add_constant(X)
model_params = np.hstack([np.array([model.intercept_]), model.coef_])
else:
x = X
model_params = model.coef_
#y = np.array(y).ravel()
# define the OLS model
olsModel = sm.OLS(y, x)
pinv_wexog,_ = pinv_extended(x)
normalized_cov_params = np.dot(pinv_wexog, np.transpose(pinv_wexog))
return sm.regression.linear_model.OLSResults(olsModel, model_params, normalized_cov_params)
如何使用？
from sklearn.linear_model import Ridge
skridge = Ridge(alpha=0.2, max_iter=9000, tol=1e-5, fit_intercept=True)
skridge.fit(X,y)
result = regression_analysis(X, y, skridge)
result.summary()