タイタニック(ロジスティック回帰)

ロジスティック回帰モデル ～タイタニック生存～

import pandas as pd
from pandas import DataFrame
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.linear_model import LogisticRegression
%matplotlib inline

# データの確認
titanic_df = pd.read_csv('data/titanic_train.csv')
titanic_df.head()

titanic_df.info()

# 不要(と思われる)列の削除
titanic_df.drop(['PassengerId', 'Name', 'Ticket', 'Cabin'], axis=1, inplace=True)
titanic_df.head()

#Ageカラムのnullを中央値で補完
titanic_df['AgeFill'] = titanic_df['Age'].fillna(titanic_df['Age'].mean())

#nullを含んでいる行を表示
titanic_df[titanic_df.isnull().any(1)]

1変数からの予測

# チケット価格から運賃を予想
data1 = titanic_df.loc[:, ["Fare"]].values
label1 = titanic_df.loc[:,["Survived"]].values

# シグモイド関数
def sigmoid(x):
     return 1 / (1+np.exp(-x))

model = LogisticRegression()
model.fit(data1, label1)

# 決定関数値（絶対値が大きいほど識別境界から離れている）
X_test_value = model.decision_function(data1) 

# 決定関数値をシグモイド関数で確率に変換
X_test_prob = sigmoid(X_test_value) 

print (model.intercept_)
print (model.coef_)

[-0.93290045]
[[0.01506685]]

w_0 = model.intercept_[0]
w_1 = model.coef_[0,0]

def sigmoid2(x):
    return 1 / (1+np.exp(-(w_1*x+w_0)))

# -1 ~ 500 まで 3000分割
x_range = np.linspace(-1, 500, 3000)

# 新規のウィンドウを描画(引数: 図のサイズ。数字はインチ。デフォルトが(8,6))
plt.figure(figsize=(9,5))
#　漫画風にする(xkcd: 世界で最も人気のあるWEB漫画)
plt.xkcd()

plt.plot(data1,np.zeros(len(data1)), 'o')
plt.plot(data1, model.predict_proba(data1), 'o')
plt.plot(x_range, sigmoid2(x_range), '-')

# グラフからなんとんく60辺りが境界っぽい

[<matplotlib.lines.Line2D at 0x1d33f424470>]

model.predict([[61]])

array([0], dtype=int64)

model.predict([[62]])

array([1], dtype=int64)

2変数からの予測

titanic_df['Gender'] = titanic_df['Sex'].map({'female': 0, 'male': 1}).astype(int)
titanic_df['Pclass_Gender'] = titanic_df['Pclass'] + titanic_df['Gender']
titanic_df.head()

	Survived	Pclass	Sex	Age	SibSp	Parch	Fare	Embarked	AgeFill	Gender	Pclass_Gender
0	0	3	male	22.0	1	0	7.2500	S	22.0	1	4
1	1	1	female	38.0	1	0	71.2833	C	38.0	0	1
2	1	3	female	26.0	0	0	7.9250	S	26.0	0	3
3	1	1	female	35.0	1	0	53.1000	S	35.0	0	1
4	0	3	male	35.0	0	0	8.0500	S	35.0	1	4

titanic_df = titanic_df.drop(['Pclass', 'Sex', 'Gender','Age'], axis=1)
titanic_df.head()

	Survived	SibSp	Parch	Fare	Embarked	AgeFill	Pclass_Gender
0	0	1	0	7.2500	S	22.0	4
1	1	1	0	71.2833	C	38.0	1
2	1	0	0	7.9250	S	26.0	3
3	1	1	0	53.1000	S	35.0	1
4	0	0	0	8.0500	S	35.0	4

np.random.seed = 0

xmin, xmax = -5, 85
ymin, ymax = 0.5, 4.5

index_survived = titanic_df[titanic_df["Survived"]==0].index
index_notsurvived = titanic_df[titanic_df["Survived"]==1].index

np.random.seed = 0

xmin, xmax = -5, 85
ymin, ymax = 0.5, 4.5

index_survived = titanic_df[titanic_df["Survived"]==0].index
index_notsurvived = titanic_df[titanic_df["Survived"]==1].index

from matplotlib.colors import ListedColormap
fig, ax = plt.subplots()
cm = plt.cm.RdBu
cm_bright = ListedColormap(['#FF0000', '#0000FF'])
sc = ax.scatter(titanic_df.loc[index_survived, 'AgeFill'],
                titanic_df.loc[index_survived, 'Pclass_Gender']+(np.random.rand(len(index_survived))-0.5)*0.1,
                color='r', label='Not Survived', alpha=0.3)
sc = ax.scatter(titanic_df.loc[index_notsurvived, 'AgeFill'],
                titanic_df.loc[index_notsurvived, 'Pclass_Gender']+(np.random.rand(len(index_notsurvived))-0.5)*0.1,
                color='b', label='Survived', alpha=0.3)
ax.set_xlabel('AgeFill')
ax.set_ylabel('Pclass_Gender')
ax.set_xlim(xmin, xmax)
ax.set_ylim(ymin, ymax)
ax.legend(bbox_to_anchor=(1.4, 1.03))

# グラフからなんとんくPclass_Gender2かつ40歳以下と
# Pclass_Gender3かつ15歳以下辺りが境界っぽい

<matplotlib.legend.Legend at 0x1d34193ba90>

data2 = titanic_df.loc[:, ["AgeFill", "Pclass_Gender"]].values
label2 =  titanic_df.loc[:,["Survived"]].values

data2

array([[22.        ,  4.        ],
       [38.        ,  1.        ],
       [26.        ,  3.        ],
       ...,
       [29.69911765,  3.        ],
       [26.        ,  2.        ],
       [32.        ,  4.        ]])

model2 = LogisticRegression()
model2.fit(data2, label2)

C:\Users\taka0\Anaconda3\lib\site-packages\sklearn\linear_model\logistic.py:433: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.
  FutureWarning)
C:\Users\taka0\Anaconda3\lib\site-packages\sklearn\utils\validation.py:761: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  y = column_or_1d(y, warn=True)





LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
          intercept_scaling=1, max_iter=100, multi_class='warn',
          n_jobs=None, penalty='l2', random_state=None, solver='warn',
          tol=0.0001, verbose=0, warm_start=False)

h = 0.02
xmin, xmax = -5, 85
ymin, ymax = 0.5, 4.5
xx, yy = np.meshgrid(np.arange(xmin, xmax, h), np.arange(ymin, ymax, h))
Z = model2.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]
Z = Z.reshape(xx.shape)

fig, ax = plt.subplots()
levels = np.linspace(0, 1.0)
cm = plt.cm.RdBu
cm_bright = ListedColormap(['#FF0000', '#0000FF'])
#contour = ax.contourf(xx, yy, Z, cmap=cm, levels=levels, alpha=0.5)

sc = ax.scatter(titanic_df.loc[index_survived, 'AgeFill'],
                titanic_df.loc[index_survived, 'Pclass_Gender']+(np.random.rand(len(index_survived))-0.5)*0.1,
                color='r', label='Not Survived', alpha=0.3)
sc = ax.scatter(titanic_df.loc[index_notsurvived, 'AgeFill'],
                titanic_df.loc[index_notsurvived, 'Pclass_Gender']+(np.random.rand(len(index_notsurvived))-0.5)*0.1,
                color='b', label='Survived', alpha=0.3)

ax.set_xlabel('AgeFill')
ax.set_ylabel('Pclass_Gender')
ax.set_xlim(xmin, xmax)
ax.set_ylim(ymin, ymax)
#fig.colorbar(contour)

x1 = xmin
x2 = xmax
y1 = -1*(model2.intercept_[0]+model2.coef_[0][0]*xmin)/model2.coef_[0][1]
y2 = -1*(model2.intercept_[0]+model2.coef_[0][0]*xmax)/model2.coef_[0][1]
ax.plot([x1, x2] ,[y1, y2], 'k--')

[<matplotlib.lines.Line2D at 0x1d34196c7f0>]

model2.predict([[12, 3]])

array([0], dtype=int64)

model2.predict([[11, 3]])

array([1], dtype=int64)

model2.predict([[47, 2]])

array([1], dtype=int64)

model2.predict([[48, 2]])

array([0], dtype=int64)

モデルの評価

from sklearn.model_selection import train_test_split

traindata1, testdata1, trainlabel1, testlabel1 = train_test_split(data1, label1, test_size=0.2)
traindata1.shape

(712, 1)

# 簡易的に別々に分割
traindata2, testdata2, trainlabel2, testlabel2 = train_test_split(data2, label2, test_size=0.2)
traindata2.shape

(712, 2)

data = titanic_df.loc[:, ].values
label =  titanic_df.loc[:,["Survived"]].values
traindata, testdata, trainlabel, testlabel = train_test_split(data, label, test_size=0.2)

eval_model1=LogisticRegression()
eval_model2=LogisticRegression()

predictor_eval1=eval_model1.fit(traindata1, trainlabel1).predict(testdata1)
predictor_eval2=eval_model2.fit(traindata2, trainlabel2).predict(testdata2)

C:\Users\taka0\Anaconda3\lib\site-packages\sklearn\linear_model\logistic.py:433: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.
  FutureWarning)
C:\Users\taka0\Anaconda3\lib\site-packages\sklearn\utils\validation.py:761: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  y = column_or_1d(y, warn=True)
C:\Users\taka0\Anaconda3\lib\site-packages\sklearn\linear_model\logistic.py:433: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.
  FutureWarning)
C:\Users\taka0\Anaconda3\lib\site-packages\sklearn\utils\validation.py:761: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  y = column_or_1d(y, warn=True)

全体的にmodel2(2変数)のほうがスコアがいい

eval_model1.score(traindata1, trainlabel1)

0.6474719101123596

eval_model1.score(testdata1,testlabel1)

0.7318435754189944

eval_model2.score(traindata2, trainlabel2)

0.7710674157303371

eval_model2.score(testdata2,testlabel2)

0.7653631284916201

from sklearn import metrics
print(metrics.classification_report(testlabel1, predictor_eval1))
print(metrics.classification_report(testlabel2, predictor_eval2))

              precision    recall  f1-score   support

           0       0.74      0.93      0.82       121
           1       0.69      0.31      0.43        58

   micro avg       0.73      0.73      0.73       179
   macro avg       0.72      0.62      0.63       179
weighted avg       0.72      0.73      0.70       179

              precision    recall  f1-score   support

           0       0.81      0.84      0.82       118
           1       0.67      0.62      0.64        61

   micro avg       0.77      0.77      0.77       179
   macro avg       0.74      0.73      0.73       179
weighted avg       0.76      0.77      0.76       179

precision, recall, f1-scoreという代表的な評価指標と、support（＝y_trueに含まれるデータ数）が、クラスごとと全体の各種平均で出ている。

from sklearn.metrics import confusion_matrix
confusion_matrix1=confusion_matrix(testlabel1, predictor_eval1)
confusion_matrix2=confusion_matrix(testlabel2, predictor_eval2)

confusion_matrix1

array([[113,   8],
       [ 40,  18]], dtype=int64)

confusion_matrix2

array([[99, 19],
       [23, 38]], dtype=int64)

fig = plt.figure(figsize = (7,7))
#plt.title(title)
sns.heatmap(
    confusion_matrix1,
    vmin=None,
    vmax=None,
    cmap="Blues",
    center=None,
    robust=False,
    annot=True, fmt='.2g',
    annot_kws=None,
    linewidths=0,
    linecolor='white',
    cbar=True,
    cbar_kws=None,
    cbar_ax=None,
    square=True, ax=None, 
    #xticklabels=columns,
    #yticklabels=columns,
    mask=None)

<matplotlib.axes._subplots.AxesSubplot at 0x1d3429988d0>

fig = plt.figure(figsize = (7,7))
#plt.title(title)
sns.heatmap(
    confusion_matrix2,
    vmin=None,
    vmax=None,
    cmap="Blues",
    center=None,
    robust=False,
    annot=True, fmt='.2g',
    annot_kws=None,
    linewidths=0,
    linecolor='white',
    cbar=True,
    cbar_kws=None,
    cbar_ax=None,
    square=True, ax=None, 
    #xticklabels=columns,
    #yticklabels=columns,
    mask=None)

<matplotlib.axes._subplots.AxesSubplot at 0x1d3423b7a90>

import seaborn as sns
sns.set(style="whitegrid")

# Load the example Titanic dataset
titanic = sns.load_dataset("titanic")

# Set up a grid to plot survival probability against several variables
g = sns.PairGrid(titanic, y_vars="survived",
                 x_vars=["class", "sex", "who", "alone"],
                 size=5, aspect=.5)

# Draw a seaborn pointplot onto each Axes
g.map(sns.pointplot, color=sns.xkcd_rgb["plum"])
g.set(ylim=(0, 1))
sns.despine(fig=g.fig, left=True)

plt.show()

C:\Users\taka0\Anaconda3\lib\site-packages\seaborn\axisgrid.py:1241: UserWarning: The `size` paramter has been renamed to `height`; please update your code.
  warnings.warn(UserWarning(msg))
C:\Users\taka0\Anaconda3\lib\site-packages\scipy\stats\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval

import seaborn as sns
sns.set(style="darkgrid")

# Load the example titanic dataset
df = sns.load_dataset("titanic")

# Make a custom palette with gendered colors
pal = dict(male="#6495ED", female="#F08080")

# Show the survival proability as a function of age and sex
g = sns.lmplot(x="age", y="survived", col="sex", hue="sex", data=df,
               palette=pal, y_jitter=.02, logistic=True)
g.set(xlim=(0, 80), ylim=(-.05, 1.05))
plt.show()