ML之LassoR&RidgeR：基于datasets糖尿病数据集利用LassoR和RidgeR算法(alpha调参)进行(9→1)回归预测
目录
基于datasets糖尿病数据集利用LassoR和RidgeR算法(alpha调参)进行(9→1)回归预测
设计思路
输出结果
核心代码
相关文章
ML之LassoR&RidgeR：基于datasets糖尿病数据集利用LassoR和RidgeR算法(alpha调参)进行(9→1)回归预测
ML之LassoR&RidgeR：基于datasets糖尿病数据集利用LassoR和RidgeR算法(alpha调参)进行(9→1)回归预测实现
基于datasets糖尿病数据集利用LassoR和RidgeR算法(alpha调参)进行(9→1)回归预测
设计思路
输出结果
.. _diabetes_dataset:Diabetes dataset----------------Ten baseline variables, age, sex, body mass index, average bloodpressure, and six blood serum measurements were obtained for each of n =442 diabetes patients, as well as the response of interest, aquantitative measure of disease progression one year after baseline.**Data Set Characteristics:**:Number of Instances: 442:Number of Attributes: First 10 columns are numeric predictive values:Target: Column 11 is a quantitative measure of disease progression one year after baseline:Attribute Information:- ageage in years- sex- bmibody mass index- bpaverage blood pressure- s1tc, T-Cells (a type of white blood cells)- s2ldl, low-density lipoproteins- s3hdl, high-density lipoproteins- s4tch, thyroid stimulating hormone- s5ltg, lamotrigine- s6glu, blood sugar levelNote: Each of these 10 feature variables have been mean centered and scaled by the standard deviation times `n_samples` (i.e. the sum of squares of each column totals 1).Source URL:https://www4.stat.ncsu.edu/~boos/var.select/diabetes.htmlFor more information see:Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani () "Least Angle Regression," Annals of Statistics (with discussion), 407-499.(https://web.stanford.edu/~hastie/Papers/LARS/LeastAngle_2002.pdf)age sex bmi bp ... s4 s5 s6 target0 0.038076 0.050680 0.061696 0.021872 ... -0.002592 0.019908 -0.017646 151.01 -0.001882 -0.044642 -0.051474 -0.026328 ... -0.039493 -0.068330 -0.092204 75.02 0.085299 0.050680 0.044451 -0.005671 ... -0.002592 0.002864 -0.025930 141.03 -0.089063 -0.044642 -0.011595 -0.036656 ... 0.034309 0.022692 -0.009362 206.04 0.005383 -0.044642 -0.036385 0.021872 ... -0.002592 -0.031991 -0.046641 135.0[5 rows x 11 columns]alphas: 50 [1.00000000e-03 1.16779862e-03 1.36375363e-03 1.59258961e-031.85982395e-03 2.17189985e-03 2.53634166e-03 2.96193630e-033.45894513e-03 4.03935136e-03 4.71714896e-03 5.50868007e-036.43302900e-03 7.51248241e-03 8.77306662e-03 1.02451751e-021.19643014e-02 1.39718947e-02 1.63163594e-02 1.90542221e-022.22514943e-02 2.59852645e-02 3.03455561e-02 3.54374986e-024.13838621e-02 4.83280172e-02 5.64373920e-02 6.59075087e-027.69666979e-02 8.98816039e-02 1.04963613e-01 1.22576363e-011.43144508e-01 1.67163960e-01 1.95213842e-01 2.27970456e-012.66223585e-01 3.10895536e-01 3.63063379e-01 4.23984915e-014.95129000e-01 5.78210965e-01 6.75233969e-01 7.88537299e-019.20852773e-01 1.07537060e+00 1.25581631e+00 1.46654056e+001.71262404e+00 2.00000000e+00]{'alpha': 0.07696669794067007}0.472 (+/-0.177) for {'alpha': 0.0010000000000000002}0.472 (+/-0.177) for {'alpha': 0.0011677986237376523}0.472 (+/-0.177) for {'alpha': 0.0013637536256035543}0.472 (+/-0.177) for {'alpha': 0.0015925896070970653}0.472 (+/-0.177) for {'alpha': 0.0018598239513468405}0.472 (+/-0.176) for {'alpha': 0.002171899850777162}0.472 (+/-0.176) for {'alpha': 0.0025363416566335814}0.472 (+/-0.176) for {'alpha': 0.002961936295945173}0.472 (+/-0.176) for {'alpha': 0.0034589451300033745}0.472 (+/-0.176) for {'alpha': 0.004039351362401994}0.472 (+/-0.176) for {'alpha': 0.004717148961805858}0.472 (+/-0.176) for {'alpha': 0.0055086800655623795}0.472 (+/-0.176) for {'alpha': 0.00643302899917478}0.472 (+/-0.176) for {'alpha': 0.007512482411700719}0.471 (+/-0.175) for {'alpha': 0.008773066621237415}0.471 (+/-0.174) for {'alpha': 0.010245175126239786}0.471 (+/-0.174) for {'alpha': 0.011964301412374057}0.472 (+/-0.173) for {'alpha': 0.013971894723352857}0.472 (+/-0.173) for {'alpha': 0.016316359428938842}0.473 (+/-0.172) for {'alpha': 0.01905422208552364}0.473 (+/-0.171) for {'alpha': 0.02225149432786609}0.474 (+/-0.170) for {'alpha': 0.025985264452188187}0.474 (+/-0.169) for {'alpha': 0.03034555606472431}0.475 (+/-0.167) for {'alpha': 0.03543749860893881}0.476 (+/-0.166) for {'alpha': 0.04138386210422369}0.477 (+/-0.164) for {'alpha': 0.04832801721026122}0.477 (+/-0.162) for {'alpha': 0.05643739198611263}0.478 (+/-0.160) for {'alpha': 0.06590750868872472}0.478 (+/-0.157) for {'alpha': 0.07696669794067007}0.477 (+/-0.154) for {'alpha': 0.08988160392874607}0.476 (+/-0.151) for {'alpha': 0.10496361336732249}0.475 (+/-0.148) for {'alpha': 0.12257636323289021}0.472 (+/-0.145) for {'alpha': 0.1431445082861357}0.469 (+/-0.143) for {'alpha': 0.1671639597721522}0.466 (+/-0.139) for {'alpha': 0.19521384216045554}0.462 (+/-0.134) for {'alpha': 0.22797045620951942}0.455 (+/-0.129) for {'alpha': 0.2662235850143214}0.447 (+/-0.126) for {'alpha': 0.31089553618622834}0.441 (+/-0.122) for {'alpha': 0.3630633792844568}0.434 (+/-0.117) for {'alpha': 0.42398491465793015}0.425 (+/-0.112) for {'alpha': 0.49512899982305664}0.412 (+/-0.107) for {'alpha': 0.5782109645659657}0.395 (+/-0.105) for {'alpha': 0.675233968650155}0.374 (+/-0.103) for {'alpha': 0.7885372992905638}0.348 (+/-0.102) for {'alpha': 0.9208527728773261}0.314 (+/-0.095) for {'alpha': 1.075370600831142}0.272 (+/-0.089) for {'alpha': 1.2558163076585396}0.212 (+/-0.084) for {'alpha': 1.466540555750942}0.129 (+/-0.087) for {'alpha': 1.7126240426614014}0.018 (+/-0.098) for {'alpha': 2.0}m_log_alphas: 100 [-0.77418297 -0.70440767 -0.63463236 -0.56485706 -0.49508175 -0.42530644-0.35553114 -0.28575583 -0.21598053 -0.14620522 -0.07642991 -0.006654610.0631207 0.132896 0.20267131 0.27244662 0.34222192 0.411997230.48177253 0.55154784 0.62132314 0.69109845 0.76087376 0.830649060.90042437 0.97019967 1.03997498 1.10975029 1.17952559 1.24930091.3190762 1.38885151 1.45862681 1.52840212 1.59817743 1.667952731.73772804 1.80750334 1.87727865 1.94705396 2.01682926 2.086604572.15637987 2.22615518 2.29593048 2.36570579 2.4354811 2.50525642.57503171 2.64480701 2.71458232 2.78435763 2.85413293 2.923908242.99368354 3.06345885 3.13323415 3.20300946 3.27278477 3.342560073.41233538 3.48211068 3.55188599 3.6216613 3.6914366 3.761211913.83098721 3.90076252 3.97053783 4.04031313 4.11008844 4.179863744.24963905 4.31941435 4.38918966 4.45896497 4.52874027 4.598515584.66829088 4.73806619 4.8078415 4.8776168 4.94739211 5.017167415.08694272 5.15671802 5.22649333 5.29626864 5.36604394 5.435819255.50559455 5.57536986 5.64514517 5.71492047 5.78469578 5.854471085.92424639 5.99402169 6.063797 6.13357231]交叉验证选择的alpha: 0.06176875494949271(100, 10) (100,)alphas: 50 [1.00000000e-04 1.22398508e-04 1.49813947e-04 1.83370035e-042.24442186e-04 2.74713886e-04 3.36245696e-04 4.11559714e-045.03742947e-04 6.16573850e-04 7.54677190e-04 9.23713617e-041.13061168e-03 1.38385182e-03 1.69381398e-03 2.07320303e-032.53756957e-03 3.10594728e-03 3.80163312e-03 4.65314220e-035.69537661e-03 6.97105597e-03 8.53246847e-03 1.04436141e-021.27828277e-02 1.56459904e-02 1.91504587e-02 2.34398757e-022.86900580e-02 3.51162028e-02 4.29817081e-02 5.26089693e-026.43925932e-02 7.88155731e-02 9.64690852e-02 1.18076721e-011.44524144e-01 1.76895395e-01 2.16517323e-01 2.65013972e-013.24373147e-01 3.97027891e-01 4.85956213e-01 5.94803152e-017.28030181e-01 8.91098077e-01 1.09069075e+00 1.33498920e+001.63400685e+00 2.00000000e+00]m_log_alphas: 50 [ 9.21034037 9.00822838 8.80611639 8.6040044 8.40189241 8.199780427.99766843 7.79555644 7.59344445 7.39133245 7.18922046 6.987108476.78499648 6.58288449 6.3807725 6.17866051 5.97654852 5.774436535.57232454 5.37021255 5.16810055 4.96598856 4.76387657 4.561764584.35965259 4.1575406 3.95542861 3.75331662 3.55120463 3.349092643.14698065 2.94486866 2.74275666 2.54064467 2.33853268 2.136420691.9343087 1.73219671 1.53008472 1.32797273 1.12586074 0.923748750.72163676 0.51952476 0.31741277 0.11530078 -0.08681121 -0.2889232-0.49103519 -0.69314718]交叉验证选择的alpha: 0.004653142170295
核心代码
class Ridge Found at: sklearn.linear_model._ridgeclass Ridge(MultiOutputMixin, RegressorMixin, _BaseRidge):"""Linear least squares with l2 regularization.Minimizes the objective function::||y - Xw||^2_2 + alpha * ||w||^2_2This model solves a regression model where the loss function isthe linear least squares function and regularization is given bythe l2-norm. Also known as Ridge Regression or Tikhonov regularization.This estimator has built-in support for multi-variate regression(i.e., when y is a 2d-array of shape (n_samples, n_targets)).Read more in the :ref:`User Guide <ridge_regression>`.Parameters----------alpha : {float, ndarray of shape (n_targets,)}, default=1.0Regularization strength; must be a positive float. Regularizationimproves the conditioning of the problem and reduces the variance ofthe estimates. Larger values specify stronger regularization.Alpha corresponds to ``1 / (2C)`` in other linear models such as:class:`~sklearn.linear_model.LogisticRegression` or:class:`sklearn.svm.LinearSVC`. If an array is passed, penalties areassumed to be specific to the targets. Hence they must correspond innumber.fit_intercept : bool, default=TrueWhether to fit the intercept for this model. If setto false, no intercept will be used in calculations(i.e. ``X`` and ``y`` are expected to be centered).normalize : bool, default=FalseThis parameter is ignored when ``fit_intercept`` is set to False.If True, the regressors X will be normalized before regression bysubtracting the mean and dividing by the l2-norm.If you wish to standardize, please use:class:`sklearn.preprocessing.StandardScaler` before calling ``fit``on an estimator with ``normalize=False``.copy_X : bool, default=TrueIf True, X will be copied; else, it may be overwritten.max_iter : int, default=NoneMaximum number of iterations for conjugate gradient solver.For 'sparse_cg' and 'lsqr' solvers, the default value is determinedby scipy.sparse.linalg. For 'sag' solver, the default value is 1000.tol : float, default=1e-3Precision of the solution.solver : {'auto', 'svd', 'cholesky', 'lsqr', 'sparse_cg', 'sag', 'saga'}, \default='auto'Solver to use in the computational routines:- 'auto' chooses the solver automatically based on the type of data.- 'svd' uses a Singular Value Decomposition of X to compute the Ridgecoefficients. More stable for singular matrices than 'cholesky'.- 'cholesky' uses the standard scipy.linalg.solve function toobtain a closed-form solution.- 'sparse_cg' uses the conjugate gradient solver as found inscipy.sparse.linalg.cg. As an iterative algorithm, this solver ismore appropriate than 'cholesky' for large-scale data(possibility to set `tol` and `max_iter`).- 'lsqr' uses the dedicated regularized least-squares routinescipy.sparse.linalg.lsqr. It is the fastest and uses an iterativeprocedure.- 'sag' uses a Stochastic Average Gradient descent, and 'saga' usesits improved, unbiased version named SAGA. Both methods also use aniterative procedure, and are often faster than other solvers whenboth n_samples and n_features are large. Note that 'sag' and'saga' fast convergence is only guaranteed on features withapproximately the same scale. You can preprocess the data with ascaler from sklearn.preprocessing.All last five solvers support both dense and sparse data. However, only'sag' and 'sparse_cg' supports sparse input when `fit_intercept` isTrue... versionadded:: 0.17Stochastic Average Gradient descent solver... versionadded:: 0.19SAGA solver.random_state : int, RandomState instance, default=NoneUsed when ``solver`` == 'sag' or 'saga' to shuffle the data.See :term:`Glossary <random_state>` for details... versionadded:: 0.17`random_state` to support Stochastic Average Gradient.Attributes----------coef_ : ndarray of shape (n_features,) or (n_targets, n_features)Weight vector(s).intercept_ : float or ndarray of shape (n_targets,)Independent term in decision function. Set to 0.0 if``fit_intercept = False``.n_iter_ : None or ndarray of shape (n_targets,)Actual number of iterations for each target. Available only forsag and lsqr solvers. Other solvers will return None... versionadded:: 0.17See also--------RidgeClassifier : Ridge classifierRidgeCV : Ridge regression with built-in cross validation:class:`sklearn.kernel_ridge.KernelRidge` : Kernel ridge regressioncombines ridge regression with the kernel trickExamples-------->>> from sklearn.linear_model import Ridge>>> import numpy as np>>> n_samples, n_features = 10, 5>>> rng = np.random.RandomState(0)>>> y = rng.randn(n_samples)>>> X = rng.randn(n_samples, n_features)>>> clf = Ridge(alpha=1.0)>>> clf.fit(X, y)Ridge()"""@_deprecate_positional_argsdef __init__(self, alpha=1.0, *, fit_intercept=True, normalize=False, copy_X=True, max_iter=None, tol=1e-3, solver="auto", random_state=None):super().__init__(alpha=alpha, fit_intercept=fit_intercept, normalize=normalize, copy_X=copy_X, max_iter=max_iter, tol=tol, solver=solver, random_state=random_state)def fit(self, X, y, sample_weight=None):"""Fit Ridge regression model.Parameters----------X : {ndarray, sparse matrix} of shape (n_samples, n_features)Training datay : ndarray of shape (n_samples,) or (n_samples, n_targets)Target valuessample_weight : float or ndarray of shape (n_samples,), default=NoneIndividual weights for each sample. If given a float, every samplewill have the same weight.Returns-------self : returns an instance of self."""return super().fit(X, y, sample_weight=sample_weight)
