思維導圖學習筆記

自己參考BoBo老師課程講解實現：

# -*- coding: utf-8 -*-
import numpy as np
from metrics import r2_score


class LinearRegression(object):
    def __int__(self):
        self.coef_ = None  # 表示係數
        self.intercept_ = None  # 表示截距
        self._theta = None  # 過程計算值，不需要暴露給外面

    def fit(self, X_train, y_train):
        """根據訓練資料集X_train, y_train訓練Linear Regression模型"""
        assert X_train is not None and y_train is not None, "訓練集X和Y不能為空"
        assert X_train.shape[0] == y_train.shape[0], "訓練集X和Y的樣本數要相等"
        # np.linalg.inv(X) 表示求X的逆矩陣

        # 不能忘了X要增加一列，第一列資料為0
        ones = np.ones(shape=(len(X_train), 1))
        X_train = np.hstack((ones, X_train))
        self._theta = np.linalg.inv(X_train.T.dot(X_train)).dot(X_train.T).dot(y_train)
        self.intercept_ = self._theta[0]
        self.coef_ = self._theta[1:]

    def _predict(self, X):
        return X.dot(self.coef_.T) + self.intercept_

    def predict1(self, X_test):
        """給定待預測資料集X_test，返回表示X_test的結果向量"""
        assert X_test.shape[1] == self.coef_.shape[0], '測試集X的特徵值個數不對'
        return np.array([self._predict(X) for X in X_test])

    def predict(self, X_test):
        """給定待預測資料集X_test，返回表示X_test的結果向量"""
        assert X_test.shape[1] == self.coef_.shape[0], '測試集X的特徵值個數不對'
        ones = np.ones(shape=(len(X_test), 1))
        X_test = np.hstack((ones, X_test))
        return X_test.dot(self._theta)

    def scores(self, X_test, y_test):
        """根據測試資料集 X_test 和 y_test 確定當前模型的準確度"""
        assert X_test.shape[0] == y_test.shape[0], '測試集X和Y的個數不相等'
        return r2_score(y_test, self.predict1(X_test))
 

測試指令碼：

# -*- encoding: utf-8 -*-
from sklearn.datasets import load_boston
from model_selection import train_test_split

from linearregression import LinearRegression

boston = load_boston()

X = boston.data
y = boston.target
X = X[y < 50]
y = y[y < 50]

X_train, X_test, y_train, y_test = train_test_split(X, y, seed=666)

lrg = LinearRegression()
lrg.fit(X_train, y_train)

# 為什麼求出來的theta.shape== (13L,)
print lrg.coef_
print lrg.intercept_

print (lrg.scores(X_test, y_test))
 

執行結果：

[-1.18919477e-01  3.63991462e-02 -3.56494193e-02  5.66737830e-02
 -1.16195486e+01  3.42022185e+00 -2.31470282e-02 -1.19509560e+00
  2.59339091e-01 -1.40112724e-02 -8.36521175e-01  7.92283639e-03
 -3.81966137e-01]
34.16143549624022
0.8129802602658537

實現總結：

1、上面的準確率是81.29%

2、在實現過程中，fit方法裡面，忘了在X_train訓練集中新增1的列向量，導致計算出來的係數矩陣引數不對

3、在pridect中，有兩種實現方法，可以直接利用中間計算出來的theta值，也可以用X_test.dot(係數矩陣) + 截距舉證

4、 np.hstack這個方法，引數值一個tuple，同時要注意相互之間的順序，越是前面的矩陣則在合併後矩陣越靠前

5、在numpy中實現一個矩陣的逆矩陣用到的方法是np.linalg.inv方法

sklearn中的迴歸實現

# -*- encoding: utf-8 -*-
from sklearn.datasets import load_boston

from sklearn.neighbors import KNeighborsRegressor
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split, GridSearchCV

def test_regression():

    boston = load_boston()
    X = boston.data
    y = boston.target
    X = X[y < 50]
    y = y[y < 50]
    X_train, X_test, y_train, y_test = train_test_split(X, y)

    # sklearn中的利用LinearRegression
    lrg = LinearRegression()
    lrg.fit(X_train, y_train)
    print ('LinearRegression:', lrg.score(X_test, y_test))

    # 利用KNN迴歸
    knnrg = KNeighborsRegressor()
    # 利用網格搜尋找到最好的KNN引數
    param_grid = [
        {
            'weights': ['uniform'],
            'n_neighbors': [i for i in range(1, 11)]
        },
        {
            'weights': ['distance'],
            'n_neighbors': [i for i in range(1, 11)],
            'p': [i for i in range(1, 6)]
        }

    ]
    grid_search = GridSearchCV(knnrg, param_grid, n_jobs=-1, verbose=1)
    grid_search.fit(X_train, y_train)

    print 'GridSearchCV:', grid_search.best_estimator_.score(X_test, y_test)
    print 'GridSearchCV Best Params:',  grid_search.best_params_

if __name__ == '__main__':
    test_regression()

執行結果：

LinearRegression: 0.7068690903842936
Fitting 3 folds for each of 60 candidates, totalling 180 fits
[Parallel(n_jobs=-1)]: Done 180 out of 180 | elapsed:    1.3s finished
GridSearchCV: 0.6994655719704079
GridSearchCV Best Params: {'n_neighbors': 10, 'weights': 'distance', 'p': 1}

sklearn中可以看到出來，線性迴歸還是要比KNN迴歸要好。此外也要注意，在使用網格搜尋的時候，不能有grid_search.score（）方法，而是用grid_search.best_estimator_.score方法，因為兩個實現不一樣。

要是你在西安，感興趣一起學習AIOPS，歡迎加入QQ群 860794445