根据以上两篇的分析，下面我们还要对数据进行处理，观察Age和Fare两个属性，乘客的数值变化幅度较大！根据逻辑回归和梯度下降的了解，如果属性值之间scale差距较大，将对收敛速度造成较大影响，甚至不收敛！因此，我们需要运用scikit-learn里面的preprocessing模块对Age和Fare两个属性做一个scaling，即将其数值转化为[-1,1]范围内。
1 # 接下来我们将一些变化幅度较大的特征化到[-1,1]之内，这样可以加速logistic regression的收敛 2 import sklearn.preprocessing as preprocessing 3 scaler = preprocessing.StandardScaler() 4 age_scale_param = scaler.fit(df['Age']) 5 df['Age_scaled'] = scaler.fit_transform(df['Age'],age_scale_param) 6 fare_scale_param = scaler.fit(df['Fare']) 7 df['Fare_scaled'] = scaler.fit_transform(df['Fare'],fare_scale_param) 8 print(df)
|
|
PassengerId |
Survived |
Age |
SibSp |
Parch |
Fare |
Cabin_No |
Cabin_Yes |
Embarked_C |
Embarked_Q |
Embarked_S |
Sex_female |
Sex_male |
Pclass_1 |
Pclass_2 |
Pclass_3 |
Age_scaled |
Fare_scaled |
| 0 |
1 |
0 |
22.000000 |
1 |
0 |
7.2500 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
-0.561417 |
-0.502445 |
| 1 |
2 |
1 |
38.000000 |
1 |
0 |
71.2833 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0.613177 |
0.786845 |
| 2 |
3 |
1 |
26.000000 |
0 |
0 |
7.9250 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
-0.267768 |
-0.488854 |
| 3 |
4 |
1 |
35.000000 |
1 |
0 |
53.1000 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
0.392941 |
0.420730 |
| 4 |
5 |
0 |
35.000000 |
0 |
0 |
8.0500 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
0.392941 |
-0.486337 |
| 5 |
6 |
0 |
23.828953 |
0 |
0 |
8.4583 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
-0.427149 |
-0.478116 |
| 6 |
7 |
0 |
54.000000 |
0 |
0 |
51.8625 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
1.787771 |
0.395814 |
| 7 |
8 |
0 |
2.000000 |
3 |
1 |
21.0750 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
-2.029659 |
-0.224083 |
| 8 |
9 |
1 |
27.000000 |
0 |
2 |
11.1333 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
-0.194356 |
-0.424256 |
| 9 |
10 |
1 |
14.000000 |
1 |
0 |
30.0708 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
-1.148714 |
-0.042956 |
| 10 |
11 |
1 |
4.000000 |
1 |
1 |
16.7000 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
-1.882835 |
-0.312172 |
| 11 |
12 |
1 |
58.000000 |
0 |
0 |
26.5500 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
2.081420 |
-0.113846 |
| 12 |
13 |
0 |
20.000000 |
0 |
0 |
8.0500 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
-0.708241 |
-0.486337 |
| 13 |
14 |
0 |
39.000000 |
1 |
5 |
31.2750 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
0.686589 |
-0.018709 |
| 14 |
15 |
0 |
14.000000 |
0 |
0 |
7.8542 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
-1.148714 |
-0.490280 |
| 15 |
16 |
1 |
55.000000 |
0 |
0 |
16.0000 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1.861183 |
-0.326267 |
| 16 |
17 |
0 |
2.000000 |
4 |
1 |
29.1250 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
-2.029659 |
-0.061999 |
| 17 |
18 |
1 |
32.066493 |
0 |
0 |
13.0000 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
0.177586 |
-0.386671 |
| 18 |
19 |
0 |
31.000000 |
1 |
0 |
18.0000 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
0.099292 |
-0.285997 |
| 19 |
20 |
1 |
29.518205 |
0 |
0 |
7.2250 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
-0.009489 |
-0.502949 |
| 20 |
21 |
0 |
35.000000 |
0 |
0 |
26.0000 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
0.392941 |
-0.124920 |
| 21 |
22 |
1 |
34.000000 |
0 |
0 |
13.0000 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
0.319529 |
-0.386671 |
| 22 |
23 |
1 |
15.000000 |
0 |
0 |
8.0292 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
-1.075302 |
-0.486756 |
| 23 |
24 |
1 |
28.000000 |
0 |
0 |
35.5000 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
-0.120944 |
0.066360 |
| 24 |
25 |
0 |
8.000000 |
3 |
1 |
21.0750 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
-1.589186 |
-0.224083 |
| 25 |
26 |
1 |
38.000000 |
1 |
5 |
31.3875 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
0.613177 |
-0.016444 |
| 26 |
27 |
0 |
29.518205 |
0 |
0 |
7.2250 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
-0.009489 |
-0.502949 |
| 27 |
28 |
0 |
19.000000 |
3 |
2 |
263.0000 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
-0.781653 |
4.647001 |
| 28 |
29 |
1 |
22.380113 |
0 |
0 |
7.8792 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
-0.533512 |
-0.489776 |
| 29 |
30 |
0 |
27.947206 |
0 |
0 |
7.8958 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
-0.124820 |
-0.489442 |
| ... |
... |
... |
... |
... |
... |
... |
... |
... |
... |
... |
... |
... |
... |
... |
... |
... |
... |
... |
| 861 |
862 |
0 |
21.000000 |
1 |
0 |
11.5000 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
-0.634829 |
-0.416873 |
| 862 |
863 |
1 |
48.000000 |
0 |
0 |
25.9292 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
1.347299 |
-0.126345 |
| 863 |
864 |
0 |
10.888325 |
8 |
2 |
69.5500 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
-1.377148 |
0.751946 |
| 864 |
865 |
0 |
24.000000 |
0 |
0 |
13.0000 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
-0.414592 |
-0.386671 |
| 865 |
866 |
1 |
42.000000 |
0 |
0 |
13.0000 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
0.906826 |
-0.386671 |
| 866 |
867 |
1 |
27.000000 |
1 |
0 |
13.8583 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
-0.194356 |
-0.369389 |
| 867 |
868 |
0 |
31.000000 |
0 |
0 |
50.4958 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
0.099292 |
0.368295 |
| 868 |
869 |
0 |
25.977889 |
0 |
0 |
9.5000 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
-0.269391 |
-0.457142 |
| 869 |
870 |
1 |
4.000000 |
1 |
1 |
11.1333 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
-1.882835 |
-0.424256 |
| 870 |
871 |
0 |
26.000000 |
0 |
0 |
7.8958 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
-0.267768 |
-0.489442 |
| 871 |
872 |
1 |
47.000000 |
1 |
1 |
52.5542 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
1.273886 |
0.409741 |
| 872 |
873 |
0 |
33.000000 |
0 |
0 |
5.0000 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
0.246117 |
-0.547748 |
| 873 |
874 |
0 |
47.000000 |
0 |
0 |
9.0000 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
1.273886 |
-0.467209 |
| 874 |
875 |
1 |
28.000000 |
1 |
0 |
24.0000 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
-0.120944 |
-0.165189 |
| 875 |
876 |
1 |
15.000000 |
0 |
0 |
7.2250 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
-1.075302 |
-0.502949 |
| 876 |
877 |
0 |
20.000000 |
0 |
0 |
9.8458 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
-0.708241 |
-0.450180 |
| 877 |
878 |
0 |
19.000000 |
0 |
0 |
7.8958 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
-0.781653 |
-0.489442 |
| 878 |
879 |
0 |
27.947206 |
0 |
0 |
7.8958 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
-0.124820 |
-0.489442 |
| 879 |
880 |
1 |
56.000000 |
0 |
1 |
83.1583 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1.934596 |
1.025945 |
| 880 |
881 |
1 |
25.000000 |
0 |
1 |
26.0000 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
-0.341180 |
-0.124920 |
| 881 |
882 |
0 |
33.000000 |
0 |
0 |
7.8958 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
0.246117 |
-0.489442 |
| 882 |
883 |
0 |
22.000000 |
0 |
0 |
10.5167 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
-0.561417 |
-0.436671 |
| 883 |
884 |
0 |
28.000000 |
0 |
0 |
10.5000 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
-0.120944 |
-0.437007 |
| 884 |
885 |
0 |
25.000000 |
0 |
0 |
7.0500 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
-0.341180 |
-0.506472 |
| 885 |
886 |
0 |
39.000000 |
0 |
5 |
29.1250 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
0.686589 |
-0.061999 |
| 886 |
887 |
0 |
27.000000 |
0 |
0 |
13.0000 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
-0.194356 |
-0.386671 |
| 887 |
888 |
1 |
19.000000 |
0 |
0 |
30.0000 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
-0.781653 |
-0.044381 |
| 888 |
889 |
0 |
16.232379 |
1 |
2 |
23.4500 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
-0.984830 |
-0.176263 |
| 889 |
890 |
1 |
26.000000 |
0 |
0 |
30.0000 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
-0.267768 |
-0.044381 |
| 890 |
891 |
0 |
32.000000 |
0 |
0 |
7.7500 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
0.172705 |
-0.492378 |
891 rows × 18 columns
接下来我们把需要的feature字段取出来，转成numpy格式，使用scikit-learn中的LogisticRegression建模。
1 from sklearn import linear_model 2 train_df = df.filter(regex='Survived|Age_.*|SibSp|Parch|Fare_.*|Cabin_.*|Embarked_.*|Sex_.*|Pclass_.*') 3 train_np = train_df.as_matrix() 4 y = train_np[:,0] 5 X = train_np[:,1:] 6 clf = linear_model.LogisticRegression(C=1.0,penalty='l1',tol=1e-6) 7 clf.fit(X,y) 8 print(clf)
接下来我们需要对测试数据集和训练数据集做一样的操作
1 # #首先用同样的RandomForestRegressor模型填上丢失的年龄 2 data_test = pd.read_csv("test.csv") 3 data_test.loc[ (data_test.Fare.isnull()), 'Fare' ] = 0 4 5 tmp_df = data_test[['Age','Fare', 'Parch', 'SibSp', 'Pclass']] 6 null_age = tmp_df[data_test.Age.isnull()].as_matrix() 7 # 根据特征属性X预测年龄并补上 8 X = null_age[:, 1:] 9 predictedAges = rfr.predict(X) 10 data_test.loc[ (data_test.Age.isnull()), 'Age' ] = predictedAges 11 12 data_test = set_Cabin_type(data_test) 13 dummies_Cabin = pd.get_dummies(data_test['Cabin'], prefix= 'Cabin') 14 dummies_Embarked = pd.get_dummies(data_test['Embarked'], prefix= 'Embarked') 15 dummies_Sex = pd.get_dummies(data_test['Sex'], prefix= 'Sex') 16 dummies_Pclass = pd.get_dummies(data_test['Pclass'], prefix= 'Pclass') 17 18 19 df_test = pd.concat([data_test, dummies_Cabin, dummies_Embarked, dummies_Sex, dummies_Pclass], axis=1) 20 df_test.drop(['Pclass', 'Name', 'Sex', 'Ticket', 'Cabin', 'Embarked'], axis=1, inplace=True) 21 df_test['Age_scaled'] = scaler.fit_transform(df_test['Age'], age_scale_param) 22 df_test['Fare_scaled'] = scaler.fit_transform(df_test['Fare'], fare_scale_param) 23 24 test = df_test.filter(regex='Age_.*|SibSp|Parch|Fare_.*|Cabin_.*|Embarked_.*|Sex_.*|Pclass_.*') 25 predictions = clf.predict(test) 26 result = pd.DataFrame({'PassengerId':data_test['PassengerId'].as_matrix(), 'Survived':predictions.astype(np.int32)}) 27 result.to_csv("logistic_regression_predictions.csv", index=False)
最后我们将预测的结果保存在logistic_regression_predictions.csv文件里。到这里只是简单分析过后的一个baseline系统。
下面要判定一下当前模型所处状态（欠拟合或者过拟合）
这里面有个问题，前面不断地做特征工程，产生的特征越来越多，用这些特征来训练模型，会对训练集拟合得越来越好，同时也可能在逐步丧失泛化能力，从而在待测数据上表现不佳，也就是发生过拟合问题。
从另一个角度上说，如果模型在待测数据上表现不佳，除掉上述说的过拟合问题，有时候也存在欠拟合问题，也就是说在训练集上拟合的结果也不好。
对于过拟合和欠拟合，有两种优化方式：
1.过拟合
1）做一个feature selection，选较好的feature的subset来做training
2）提供更多的数据，从而弥补原始数据偏差，从而学习到的模型更准确
3）采用正则化，正则化方法包括L0正则、L1正则和L2正则，而正则一般是在目标函数之后加上对于的范数。但是在机器学习中一般使用L2正则。
2.欠拟合
1）添加其他特征项，有时候我们模型出现欠拟合的时候是因为特征项不够导致的，可以添加其他特征项来很好地解决。例如，“组合”、“泛化”、“相关性”三类特征是特征添加的重要手段。
2）添加多项式特征，这个在机器学习算法里面用的很普遍，例如将线性模型通过添加二次项或者三次项使模型泛化能力更强。
3）减少正则化参数，正则化的目的是用来防止过拟合的，但是现在模型出现了欠拟合，则需要减少正则化参数。
scikit-learn里面的learning curve可以帮助我们判定模型现在所处的状态。这里我们画一下最先得到的baseline model的learning curve。
1 import numpy as np 2 import matplotlib.pyplot as plt 3 from sklearn.learning_curve import learning_curve 4 5 #用sklearn的learning_curve得到training_score和cv_score，使用matplotlib画出learning curve 6 7 def plot_learning_curve(estimator,title,X,y,ylim=None,cv=None,n_jobs=1,train_sizes=np.linspace(.05,1.,20),verbose=0,plot=True): 8 """ 9 画出data在某模型上的learning curve. 10 参数解释 11 ---------- 12 estimator : 你用的分类器。 13 title : 表格的标题。 14 X : 输入的feature，numpy类型 15 y : 输入的target vector 16 ylim : tuple格式的(ymin, ymax), 设定图像中纵坐标的最低点和最高点 17 cv : 做cross-validation的时候，数据分成的份数，其中一份作为cv集，其余n-1份作为training(默认为3份) 18 n_jobs : 并行的的任务数(默认1) 19 """ 20 train_sizes, train_scores, test_scores = learning_curve( 21 estimator, X, y, cv=cv, n_jobs=n_jobs, train_sizes=train_sizes, verbose=verbose) 22 23 train_scores_mean = np.mean(train_scores, axis=1) 24 train_scores_std = np.std(train_scores, axis=1) 25 test_scores_mean = np.mean(test_scores, axis=1) 26 test_scores_std = np.std(test_scores, axis=1) 27 28 if plot: 29 plt.figure() 30 plt.title(title) 31 if ylim is not None: 32 plt.ylim(*ylim) 33 plt.xlabel('train_sample') 34 plt.ylabel('score') 35 plt.gca().invert_yaxis() 36 plt.grid() 37 38 plt.fill_between(train_sizes, train_scores_mean - train_scores_std, train_scores_mean + train_scores_std, 39 alpha=0.1, color="b") 40 plt.fill_between(train_sizes, test_scores_mean - test_scores_std, test_scores_mean + test_scores_std, 41 alpha=0.1, color="r") 42 plt.plot(train_sizes, train_scores_mean, 'o-', color="b", label="train_score") 43 plt.plot(train_sizes, test_scores_mean, 'o-', color="r", label="cross_validation_score") 44 45 plt.legend(loc='best') 46 plt.draw() 47 plt.gca().invert_yaxis() 48 plt.show() 49 50 midpoint = ((train_scores_mean[-1] + train_scores_std[-1]) + (test_scores_mean[-1] - test_scores_std[-1])) / 2 51 diff = (train_scores_mean[-1] + train_scores_std[-1]) - (test_scores_mean[-1] - test_scores_std[-1]) 52 return midpoint, diff 53 54 plot_learning_curve(clf, u"学习曲线", X, y)
结果如下(0.80656968448540245, 0.018258876711338634)
从得到的结果来看，尽管learn——curve没有理论推导的光滑，但是仍可以看出，训练集和交叉验证集上的得分曲线走势还是符合预期的。
目前的曲线来看，我们的model并不处于overfitting的状态（overfitting的表现一般是训练集得分高，交叉验证集得分低很多，中间的gap比较大）。因此我们可以再做些feature engineering的工作，添加一些新的特征或者组合特征到模型中。