ML之LiR&LassoR：利用boston房价数据集(PCA处理)采用线性回归和Lasso套索回归算法实现房价预测模型评估

目录

利用boston房价数据集(PCA处理)采用线性回归和Lasso套索回归算法实现房价预测模型评估

设计思路

输出结果

核心代码

利用boston房价数据集(PCA处理)采用线性回归和Lasso套索回归算法实现房价预测模型评估

设计思路

更新……

输出结果

         Id  MSSubClass MSZoning  ...  SaleType  SaleCondition SalePrice
      0   1 60 RL  ... WD Normal 208500
      1   2 20 RL  ... WD Normal 181500
      2   3 60 RL  ... WD Normal 223500
      3   4 70 RL  ... WD Abnorml 140000
      4   5 60 RL  ... WD Normal 250000
      [5 rows x 81 columns]
      numeric_columns 36 ['LotFrontage', 'LotArea', 'OverallQual', 'OverallCond', 'YearBuilt', 'YearRemodAdd', 'MasVnrArea', 'BsmtFinSF1', 'BsmtFinSF2', 'BsmtUnfSF', 'TotalBsmtSF', '1stFlrSF', '2ndFlrSF', 'LowQualFinSF', 'GrLivArea', 'BsmtFullBath', 'BsmtHalfBath', 'FullBath', 'HalfBath', 'BedroomAbvGr', 'KitchenAbvGr', 'TotRmsAbvGrd', 'Fireplaces', 'GarageYrBlt', 'GarageCars', 'GarageArea', 'WoodDeckSF', 'OpenPorchSF', 'EnclosedPorch', '3SsnPorch', 'ScreenPorch', 'PoolArea', 'MiscVal', 'MoSold', 'YrSold', 'SalePrice']
      (1460, 36)
         LotFrontage  LotArea  OverallQual  ...  MoSold  YrSold  SalePrice
      0 65.0 8450 7  ... 2 2008 208500
      1 80.0 9600 6  ... 5 2007 181500
      2 68.0 11250 7  ... 9 2008 223500
      3 60.0 9550 7  ... 2 2006 140000
      4 84.0 14260 8  ... 12 2008 250000
      依次统计每列缺失值元素个数：
      36 [259, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
      Missing_data_Per_dict_0： (33, 0.9167, {'LotArea': 0.0, 'OverallQual': 0.0, 'OverallCond': 0.0, 'YearBuilt': 0.0, 'YearRemodAdd': 0.0, 'BsmtFinSF1': 0.0, 'BsmtFinSF2': 0.0, 'BsmtUnfSF': 0.0, 'TotalBsmtSF': 0.0, '1stFlrSF': 0.0, '2ndFlrSF': 0.0, 'LowQualFinSF': 0.0, 'GrLivArea': 0.0, 'BsmtFullBath': 0.0, 'BsmtHalfBath': 0.0, 'FullBath': 0.0, 'HalfBath': 0.0, 'BedroomAbvGr': 0.0, 'KitchenAbvGr': 0.0, 'TotRmsAbvGrd': 0.0, 'Fireplaces': 0.0, 'GarageCars': 0.0, 'GarageArea': 0.0, 'WoodDeckSF': 0.0, 'OpenPorchSF': 0.0, 'EnclosedPorch': 0.0, '3SsnPorch': 0.0, 'ScreenPorch': 0.0, 'PoolArea': 0.0, 'MiscVal': 0.0, 'MoSold': 0.0, 'YrSold': 0.0, 'SalePrice': 0.0})
      Missing_data_Per_dict_Not0： (3, 0.0833, {'LotFrontage': 0.177397, 'MasVnrArea': 0.005479, 'GarageYrBlt': 0.055479})
      Missing_data_Per_dict_under01： (2, 0.0556, {'MasVnrArea': 0.005479, 'GarageYrBlt': 0.055479})
      依次计算每列缺失值元素占比： {'LotFrontage': 0.177397, 'MasVnrArea': 0.005479, 'GarageYrBlt': 0.055479}
      data_Missing_dict {'LotFrontage': 0.1773972602739726, 'LotArea': 0.0, 'OverallQual': 0.0, 'OverallCond': 0.0, 'YearBuilt': 0.0, 'YearRemodAdd': 0.0, 'MasVnrArea': 0.005479452054794521, 'BsmtFinSF1': 0.0, 'BsmtFinSF2': 0.0, 'BsmtUnfSF': 0.0, 'TotalBsmtSF': 0.0, '1stFlrSF': 0.0, '2ndFlrSF': 0.0, 'LowQualFinSF': 0.0, 'GrLivArea': 0.0, 'BsmtFullBath': 0.0, 'BsmtHalfBath': 0.0, 'FullBath': 0.0, 'HalfBath': 0.0, 'BedroomAbvGr': 0.0, 'KitchenAbvGr': 0.0, 'TotRmsAbvGrd': 0.0, 'Fireplaces': 0.0, 'GarageYrBlt': 0.05547945205479452, 'GarageCars': 0.0, 'GarageArea': 0.0, 'WoodDeckSF': 0.0, 'OpenPorchSF': 0.0, 'EnclosedPorch': 0.0, '3SsnPorch': 0.0, 'ScreenPorch': 0.0, 'PoolArea': 0.0, 'MiscVal': 0.0, 'MoSold': 0.0, 'YrSold': 0.0, 'SalePrice': 0.0}
      after dropna (1121, 36)
      <class 'numpy.ndarray'>
       LotFrontage LotArea OverallQual ... MiscVal MoSold YrSold
      0 -0.233570 -0.205885 0.570704 ... -0.141407 -1.615345 0.153084
      1 0.384834 -0.064358 -0.153825 ... -0.141407 -0.498715 -0.596291
      2 -0.109889 0.138702 0.570704 ... -0.141407 0.990125 0.153084
      3 -0.439705 -0.070512 0.570704 ... -0.141407 -1.615345 -1.345665
      4 0.549742 0.509132 1.295234 ... -0.141407 2.106755 0.153084
      ... ... ... ... ... ... ... ...
      1116 -0.357251 -0.271480 -0.153825 ... -0.141407 0.617915 -0.596291
      1117 0.590968 0.375605 -0.153825 ... -0.141407 -1.615345 1.651832
      1118 -0.192343 -0.133030 0.570704 ... 14.947388 -0.498715 1.651832
      1119 -0.109889 -0.049960 -0.878355 ... -0.141407 -0.870925 1.651832
      1120 0.178699 -0.022885 -0.878355 ... -0.141407 -0.126505 0.153084
      [1121 rows x 35 columns]
      前10个主成分解释了数据中63.80%的变化
      经过PCA后，进行第一层主成分分析-------------------------------------
      [(0.16970682313415306, 'LotFrontage'), (0.1211669980146095, 'LotArea'), (0.3008665261375608, 'OverallQual'), (-0.1017783758120348, 'OverallCond'), (0.23754113423286216, 'YearBuilt'), (0.21067267847804322, 'YearRemodAdd'), (0.19125461510335365, 'MasVnrArea'), (0.14136511574315347, 'BsmtFinSF1'), (-0.013552848692716916, 'BsmtFinSF2'), (0.11439764110410199, 'BsmtUnfSF'), (0.259354275741638, 'TotalBsmtSF'), (0.2591780447881022, '1stFlrSF'), (0.11504305093601253, '2ndFlrSF'), (0.004231304806602964, 'LowQualFinSF'), (0.2877802164879641, 'GrLivArea'), (0.08317879411803167, 'BsmtFullBath'), (-0.02114280846249704, 'BsmtHalfBath'), (0.25499633884283257, 'FullBath'), (0.11080279874459822, 'HalfBath'), (0.1017767099777179, 'BedroomAbvGr'), (-0.01012145139988125, 'KitchenAbvGr'), (0.23572236584667458, 'TotRmsAbvGrd'), (0.17611466785004926, 'Fireplaces'), (0.23726651555979883, 'GarageYrBlt'), (0.2831568046802727, 'GarageCars'), (0.279827792756442, 'GarageArea'), (0.13036585867815073, 'WoodDeckSF'), (0.16664693092097654, 'OpenPorchSF'), (-0.08602539908222213, 'EnclosedPorch'), (0.010532579475601184, '3SsnPorch'), (0.02556170369869493, 'ScreenPorch'), (0.06246570190310543, 'PoolArea'), (-0.015493399959318557, 'MiscVal'), (0.028399126033275164, 'MoSold'), (-0.011129722622237775, 'YrSold')]
      [(0.3008665261375608, 'OverallQual'), (0.2877802164879641, 'GrLivArea'), (0.2831568046802727, 'GarageCars'), (0.279827792756442, 'GarageArea'), (0.259354275741638, 'TotalBsmtSF'), (0.2591780447881022, '1stFlrSF'), (0.25499633884283257, 'FullBath'), (0.23754113423286216, 'YearBuilt'), (0.23726651555979883, 'GarageYrBlt'), (0.23572236584667458, 'TotRmsAbvGrd'), (0.21067267847804322, 'YearRemodAdd'), (0.19125461510335365, 'MasVnrArea'), (0.17611466785004926, 'Fireplaces'), (0.16970682313415306, 'LotFrontage'), (0.16664693092097654, 'OpenPorchSF'), (0.14136511574315347, 'BsmtFinSF1'), (0.13036585867815073, 'WoodDeckSF'), (0.1211669980146095, 'LotArea'), (0.11504305093601253, '2ndFlrSF'), (0.11439764110410199, 'BsmtUnfSF'), (0.11080279874459822, 'HalfBath'), (0.1017767099777179, 'BedroomAbvGr'), (0.08317879411803167, 'BsmtFullBath'), (0.06246570190310543, 'PoolArea'), (0.028399126033275164, 'MoSold'), (0.02556170369869493, 'ScreenPorch'), (0.010532579475601184, '3SsnPorch'), (0.004231304806602964, 'LowQualFinSF'), (-0.01012145139988125, 'KitchenAbvGr'), (-0.011129722622237775, 'YrSold'), (-0.013552848692716916, 'BsmtFinSF2'), (-0.015493399959318557, 'MiscVal'), (-0.02114280846249704, 'BsmtHalfBath'), (-0.08602539908222213, 'EnclosedPorch'), (-0.1017783758120348, 'OverallCond')]
      经过PCA后，进行第二层主成分分析-------------------------------------
      [(0.037140668512444255, 'LotFrontage'), (0.005762269875424171, 'LotArea'), (-0.02265545744738413, 'OverallQual'), (0.06797580738610676, 'OverallCond'), (-0.22034458100877843, 'YearBuilt'), (-0.11769773674122082, 'YearRemodAdd'), (-0.02330741979867707, 'MasVnrArea'), (-0.26830830083400875, 'BsmtFinSF1'), (-0.06776753790369254, 'BsmtFinSF2'), (0.10349973537774373, 'BsmtUnfSF'), (-0.2014230745261159, 'TotalBsmtSF'), (-0.14501101153644946, '1stFlrSF'), (0.43960496790131565, '2ndFlrSF'), (0.11932040000909688, 'LowQualFinSF'), (0.2706724094458561, 'GrLivArea'), (-0.2741406761479087, 'BsmtFullBath'), (-0.001880261013674545, 'BsmtHalfBath'), (0.12608264523927462, 'FullBath'), (0.23358978781221817, 'HalfBath'), (0.3864399252645517, 'BedroomAbvGr'), (0.12179545892853964, 'KitchenAbvGr'), (0.3371810668951179, 'TotRmsAbvGrd'), (0.06581774146310777, 'Fireplaces'), (-0.1834261688794573, 'GarageYrBlt'), (-0.04640661259007604, 'GarageCars'), (-0.08613653500685643, 'GarageArea'), (-0.047991361825782064, 'WoodDeckSF'), (0.03130768246434415, 'OpenPorchSF'), (0.13376424222015906, 'EnclosedPorch'), (-0.02564456693744644, '3SsnPorch'), (0.04211790221668751, 'ScreenPorch'), (0.03032238859229474, 'PoolArea'), (0.04968459727862472, 'MiscVal'), (0.02754218343139985, 'MoSold'), (-0.04555808126996797, 'YrSold')]
      [(0.43960496790131565, '2ndFlrSF'), (0.3864399252645517, 'BedroomAbvGr'), (0.3371810668951179, 'TotRmsAbvGrd'), (0.2706724094458561, 'GrLivArea'), (0.23358978781221817, 'HalfBath'), (0.13376424222015906, 'EnclosedPorch'), (0.12608264523927462, 'FullBath'), (0.12179545892853964, 'KitchenAbvGr'), (0.11932040000909688, 'LowQualFinSF'), (0.10349973537774373, 'BsmtUnfSF'), (0.06797580738610676, 'OverallCond'), (0.06581774146310777, 'Fireplaces'), (0.04968459727862472, 'MiscVal'), (0.04211790221668751, 'ScreenPorch'), (0.037140668512444255, 'LotFrontage'), (0.03130768246434415, 'OpenPorchSF'), (0.03032238859229474, 'PoolArea'), (0.02754218343139985, 'MoSold'), (0.005762269875424171, 'LotArea'), (-0.001880261013674545, 'BsmtHalfBath'), (-0.02265545744738413, 'OverallQual'), (-0.02330741979867707, 'MasVnrArea'), (-0.02564456693744644, '3SsnPorch'), (-0.04555808126996797, 'YrSold'), (-0.04640661259007604, 'GarageCars'), (-0.047991361825782064, 'WoodDeckSF'), (-0.06776753790369254, 'BsmtFinSF2'), (-0.08613653500685643, 'GarageArea'), (-0.11769773674122082, 'YearRemodAdd'), (-0.14501101153644946, '1stFlrSF'), (-0.1834261688794573, 'GarageYrBlt'), (-0.2014230745261159, 'TotalBsmtSF'), (-0.22034458100877843, 'YearBuilt'), (-0.26830830083400875, 'BsmtFinSF1'), (-0.2741406761479087, 'BsmtFullBath')]
      不进行PCA的线性回归的MSE是1644140595.6636596
      前10个PCA主成分进行线性回归的MSE是1836601962.4751632
      [1e-10, 1e-09, 1e-08, 1e-07, 1e-06, 1e-05, 0.0001, 0.001, 0.01, 0.1]
      [1642818822.3530025, 1642818822.3529558, 1642818822.3524888, 1642818822.3471866, 1642818822.3005185, 1642818821.7415214, 1642818817.1179569, 1642818756.7038794, 1642818283.0732899, 1642813588.5752773]
      [1e-10, 1e-09, 1e-08, 1e-07, 1e-06, 1e-05, 0.0001, 0.001, 0.01, 0.1]
      [1836601962.4751682, 1836601962.4752123, 1836601962.475657, 1836601962.480097, 1836601962.5245085, 1836601962.9652405, 1836601967.4063494, 1836602011.8174434, 1836602455.9288514, 1836606882.1034737]
  
 

核心代码

      PCA
      class TruncatedSVD Found at: sklearn.decomposition._truncated_svd
      class TruncatedSVD(TransformerMixin, BaseEstimator):
      """Dimensionality reduction using truncated SVD (aka LSA).
       This transformer performs linear dimensionality reduction by means of
       truncated singular value decomposition (SVD). Contrary to PCA, this
       estimator does not center the data before computing the singular value
       decomposition. This means it can work with sparse matrices
       efficiently.
       In particular, truncated SVD works on term count/tf-idf matrices as
       returned by the vectorizers in :mod:`sklearn.feature_extraction.text`. In
       that context, it is known as latent semantic analysis (LSA).
       This estimator supports two algorithms: a fast randomized SVD solver,
       and
       a "naive" algorithm that uses ARPACK as an eigensolver on `X * X.T` or
       `X.T * X`, whichever is more efficient.
      LinearRegression
      class LinearRegression Found at: sklearn.linear_model._base
      class LinearRegression(MultiOutputMixin, RegressorMixin, LinearModel):
       """
       Ordinary least squares Linear Regression.
       LinearRegression fits a linear model with coefficients w = (w1, ..., wp)
       to minimize the residual sum of squares between the observed targets in
       the dataset, and the targets predicted by the linear approximation.
      Lasso
      class Lasso Found at: sklearn.linear_model._coordinate_descent
      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||_1
       Technically the Lasso model is optimizing the same objective function as
       the Elastic Net with ``l1_ratio=1.0`` (no L2 penalty).
       Read more in the :ref:`User Guide <lasso>`.
  
 

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