ML之4PolyR：利用四次多項式回歸4PolyR模型+兩種正則化(Lasso/Ridge)在披薩數據集上擬合(train)、價格回歸預測(test)

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目錄

輸出結果

設計思路

核心代碼

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輸出結果

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設計思路

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核心代碼

lasso_poly4 = Lasso() lasso_poly4.fit(X_train_poly4, y_train)ridge_poly4 = Ridge() ridge_poly4.fit(X_train_poly4, y_train)

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class Lasso(ElasticNet):"""Linear Model trained with L1 prior as regularizer (aka the Lasso)The optimization objective for Lasso is::(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1Technically the Lasso model is optimizing the same objective function asthe Elastic Net with ``l1_ratio=1.0`` (no L2 penalty).Read more in the :ref:`User Guide <lasso>`.Parameters----------alpha : float, optionalConstant that multiplies the L1 term. Defaults to 1.0.``alpha = 0`` is equivalent to an ordinary least square, solvedby the :class:`LinearRegression` object. For numericalreasons, using ``alpha = 0`` with the ``Lasso`` object is not advised.Given this, you should use the :class:`LinearRegression` object.fit_intercept : booleanwhether to calculate the intercept for this model. If setto false, no intercept will be used in calculations(e.g. data is expected to be already centered).normalize : boolean, optional, 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``.precompute : True | False | array-like, default=FalseWhether to use a precomputed Gram matrix to speed upcalculations. If set to ``'auto'`` let us decide. The Grammatrix can also be passed as argument. For sparse inputthis option is always ``True`` to preserve sparsity.copy_X : boolean, optional, default TrueIf ``True``, X will be copied; else, it may be overwritten.max_iter : int, optionalThe maximum number of iterationstol : float, optionalThe tolerance for the optimization: if the updates aresmaller than ``tol``, the optimization code checks thedual gap for optimality and continues until it is smallerthan ``tol``.warm_start : bool, optionalWhen set to True, reuse the solution of the previous call to fit asinitialization, otherwise, just erase the previous solution.positive : bool, optionalWhen set to ``True``, forces the coefficients to be positive.random_state : int, RandomState instance or None, optional, default NoneThe seed of the pseudo random number generator that selects a randomfeature to update. If int, random_state is the seed used by the randomnumber generator; If RandomState instance, random_state is the randomnumber generator; If None, the random number generator is theRandomState instance used by `np.random`. Used when ``selection`` =='random'.selection : str, default 'cyclic'If set to 'random', a random coefficient is updated every iterationrather than looping over features sequentially by default. This(setting to 'random') often leads to significantly faster convergenceespecially when tol is higher than 1e-4.Attributes----------coef_ : array, shape (n_features,) | (n_targets, n_features)parameter vector (w in the cost function formula)sparse_coef_ : scipy.sparse matrix, shape (n_features, 1) | \(n_targets, n_features)``sparse_coef_`` is a readonly property derived from ``coef_``intercept_ : float | array, shape (n_targets,)independent term in decision function.n_iter_ : int | array-like, shape (n_targets,)number of iterations run by the coordinate descent solver to reachthe specified tolerance.Examples-------->>> from sklearn import linear_model>>> clf = linear_model.Lasso(alpha=0.1)>>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2])Lasso(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=1000,normalize=False, positive=False, precompute=False, random_state=None,selection='cyclic', tol=0.0001, warm_start=False)>>> print(clf.coef_)[ 0.85 0. ]>>> print(clf.intercept_)0.15See also--------lars_pathlasso_pathLassoLarsLassoCVLassoLarsCVsklearn.decomposition.sparse_encodeNotes-----The algorithm used to fit the model is coordinate descent.To avoid unnecessary memory duplication the X argument of the fit methodshould be directly passed as a Fortran-contiguous numpy array."""path = staticmethod(enet_path)def __init__(self, alpha=1.0, fit_intercept=True, normalize=False, precompute=False, copy_X=True, max_iter=1000, tol=1e-4, warm_start=False, positive=False, random_state=None, selection='cyclic'):super(Lasso, self).__init__(alpha=alpha, l1_ratio=1.0, fit_intercept=fit_intercept, normalize=normalize, precompute=precompute, copy_X=copy_X, max_iter=max_iter, tol=tol, warm_start=warm_start, positive=positive, random_state=random_state, selection=selection)############################################################################### # Functions for CV with paths functions class Ridge(_BaseRidge, RegressorMixin):"""Linear least squares with l2 regularization.This 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, array-like}, shape (n_targets)Regularization 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 ``C^-1`` in other linear models such asLogisticRegression or LinearSVC. If an array is passed, penalties areassumed to be specific to the targets. Hence they must correspond innumber.fit_intercept : booleanWhether to calculate the intercept for this model. If setto false, no intercept will be used in calculations(e.g. data is expected to be already centered).normalize : boolean, optional, 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 : boolean, optional, default TrueIf True, X will be copied; else, it may be overwritten.max_iter : int, optionalMaximum 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 : floatPrecision of the solution.solver : {'auto', 'svd', 'cholesky', 'lsqr', 'sparse_cg', 'sag', 'saga'}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 but may not be availablein old scipy versions. It also uses an iterative procedure.- '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 'saga' supports sparse input when `fit_intercept` isTrue... versionadded:: 0.17Stochastic Average Gradient descent solver... versionadded:: 0.19SAGA solver.random_state : int, RandomState instance or None, optional, default NoneThe seed of the pseudo random number generator to use when shufflingthe data. If int, random_state is the seed used by the random numbergenerator; If RandomState instance, random_state is the random numbergenerator; If None, the random number generator is the RandomStateinstance used by `np.random`. Used when ``solver`` == 'sag'... versionadded:: 0.17*random_state* to support Stochastic Average Gradient.Attributes----------coef_ : array, shape (n_features,) or (n_targets, n_features)Weight vector(s).intercept_ : float | array, shape = (n_targets,)Independent term in decision function. Set to 0.0 if``fit_intercept = False``.n_iter_ : array or None, 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, RidgeCV, :class:`sklearn.kernel_ridge.KernelRidge`Examples-------->>> from sklearn.linear_model import Ridge>>> import numpy as np>>> n_samples, n_features = 10, 5>>> np.random.seed(0)>>> y = np.random.randn(n_samples)>>> X = np.random.randn(n_samples, n_features)>>> clf = Ridge(alpha=1.0)>>> clf.fit(X, y) # doctest: +NORMALIZE_WHITESPACERidge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,normalize=False, random_state=None, solver='auto', tol=0.001)"""def __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(Ridge, self).__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 modelParameters----------X : {array-like, sparse matrix}, shape = [n_samples, n_features]Training datay : array-like, shape = [n_samples] or [n_samples, n_targets]Target valuessample_weight : float or numpy array of shape [n_samples]Individual weights for each sampleReturns-------self : returns an instance of self."""return super(Ridge, self).fit(X, y, sample_weight=sample_weight)

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