ML之LiR&LassoR：利用boston房價數據集(PCA處理)采用線性回歸和Lasso套索回歸算法實現房價預測模型評估

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目錄

利用boston房價數據集(PCA處理)采用線性回歸和Lasso套索回歸算法實現房價預測模型評估

設計思路

輸出結果

核心代碼

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利用boston房價數據集(PCA處理)采用線性回歸和Lasso套索回歸算法實現房價預測模型評估

設計思路

更新……

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輸出結果

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依次統計每列缺失值元素個數： 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}) 依次計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個主成分解釋了數據中63.80%的變化 經過PCA后，進行第一層主成分分析------------------------------------- [(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')] 經過PCA后，進行第二層主成分分析------------------------------------- [(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')] 不進行PCA的線性回歸的MSE是1644140595.6636596 前10個PCA主成分進行線性回歸的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]

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核心代碼

PCA class TruncatedSVD Found at: sklearn.decomposition._truncated_svdclass TruncatedSVD(TransformerMixin, BaseEstimator):"""Dimensionality reduction using truncated SVD (aka LSA).This transformer performs linear dimensionality reduction by means oftruncated singular value decomposition (SVD). Contrary to PCA, thisestimator does not center the data before computing the singular valuedecomposition. This means it can work with sparse matricesefficiently.In particular, truncated SVD works on term count/tf-idf matrices asreturned by the vectorizers in :mod:`sklearn.feature_extraction.text`. Inthat context, it is known as latent semantic analysis (LSA).This estimator supports two algorithms: a fast randomized SVD solver, anda "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._baseclass 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 inthe 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||_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>`.

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