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1. 通過網格搜索完善模型
在本文中,我們將爲決策樹模型擬合一些樣本數據。 這個初始模型會過擬合。 然後,我們將使用網格搜索爲這個模型找到更好的參數,以減少過擬合。
首先,導入所需要的庫:
%matplotlib inline
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
1.1 數據導入
首先定義一個函數用於讀取 csv 數據並進行可視化:
def load_pts(csv_name):
data = np.asarray(pd.read_csv(csv_name, header=None))
X = data[:,0:2]
y = data[:,2]
plt.scatter(X[np.argwhere(y==0).flatten(),0], X[np.argwhere(y==0).flatten(),1],s = 50, color = 'blue', edgecolor = 'k')
plt.scatter(X[np.argwhere(y==1).flatten(),0], X[np.argwhere(y==1).flatten(),1],s = 50, color = 'red', edgecolor = 'k')
plt.xlim(-2.05,2.05)
plt.ylim(-2.05,2.05)
plt.grid(False)
plt.tick_params(
axis='x',
which='both',
bottom='off',
top='off')
return X,y
X, y = load_pts('Data/data.csv')
plt.show()
1.2 拆分數據爲訓練集和測試集
from sklearn.model_selection import train_test_split
from sklearn.metrics import f1_score, make_scorer
#Fixing a random seed
import random
random.seed(42)
# Split the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
1.3 擬合決策樹模型
from sklearn.tree import DecisionTreeClassifier
# Define the model (with default hyperparameters)
clf = DecisionTreeClassifier(random_state=42)
# Fit the model
clf.fit(X_train, y_train)
# Make predictions
train_predictions = clf.predict(X_train)
test_predictions = clf.predict(X_test)
現在我們來可視化模型,並測試 f1_score,首先定義可視化函數:
def plot_model(X, y, clf):
# 繪製兩類點的散點圖
plt.scatter(X[np.argwhere(y==0).flatten(),0],X[np.argwhere(y==0).flatten(),1],s = 50, color = 'blue', edgecolor = 'k')
plt.scatter(X[np.argwhere(y==1).flatten(),0],X[np.argwhere(y==1).flatten(),1],s = 50, color = 'red', edgecolor = 'k')
# 圖形設置
plt.xlim(-2.05,2.05)
plt.ylim(-2.05,2.05)
plt.grid(False)
plt.tick_params(
axis='x',
which='both',
bottom='off',
top='off')
# 利用 np.meshgrid(r,r) 生成一個平面對於的橫縱座標
r = np.linspace(-2.1,2.1,300)
s,t = np.meshgrid(r,r)
# 將座標轉換爲與決策樹的訓練集相同格式
s = np.reshape(s,(np.size(s),1))
t = np.reshape(t,(np.size(t),1))
h = np.concatenate((s,t),1)
# 對平面上的每一個點進行預測類別
z = clf.predict(h)
# 將橫縱座標及對應類別轉換爲矩陣形式
s = s.reshape((np.size(r),np.size(r)))
t = t.reshape((np.size(r),np.size(r)))
z = z.reshape((np.size(r),np.size(r)))
# 利用 plt.contourf 繪製不同等高面
plt.contourf(s,t,z,colors = ['blue','red'],alpha = 0.2,levels = range(-1,2))
# 繪製等高面邊緣
if len(np.unique(z)) > 1:
plt.contour(s,t,z,colors = 'k', linewidths = 2)
plt.show()
plot_model(X, y, clf)
print('The Training F1 Score is', f1_score(train_predictions, y_train))
print('The Testing F1 Score is', f1_score(test_predictions, y_test))
The Training F1 Score is 1.0
The Testing F1 Score is 0.7000000000000001
訓練集得分爲 1 ,而測試集得分爲 0.7,可以看出當前模型有些過擬合,下面我們通過網絡搜索來優化參數。
1.4 使用網絡搜索完善模型
現在,我們將執行以下步驟:
1.首先,定義一些參數來執行網格搜索:max_depth
, min_samples_leaf
, 和 min_samples_split
。
2.使用f1_score
,爲模型製作記分器。
3.使用參數和記分器,在分類器上執行網格搜索。
4.將數據擬合到新的分類器中。
5.繪製模型並找到 f1_score。
6.如果模型不太好,則更改參數的範圍並再次擬合。
from sklearn.metrics import make_scorer
from sklearn.model_selection import GridSearchCV
clf = DecisionTreeClassifier(random_state=42)
# 生成參數列表
parameters = {'max_depth':[2,4,6,8,10],'min_samples_leaf':[2,4,6,8,10], 'min_samples_split':[2,4,6,8,10]}
# 定義計分器
scorer = make_scorer(f1_score)
# 生成網絡搜索器
grid_obj = GridSearchCV(clf, parameters, scoring=scorer)
# 擬合網絡搜索器
grid_fit = grid_obj.fit(X_train, y_train)
# 獲得最佳決策樹模型
best_clf = grid_fit.best_estimator_
# 對最佳模型進行擬合
best_clf.fit(X_train, y_train)
# 對測試集和訓練集進行預測
best_train_predictions = best_clf.predict(X_train)
best_test_predictions = best_clf.predict(X_test)
# 計算測試集得分和訓練集得分
print('The training F1 Score is', f1_score(best_train_predictions, y_train))
print('The testing F1 Score is', f1_score(best_test_predictions, y_test))
# 模型可視化
plot_model(X, y, best_clf)
# 查看最佳模型的參數設置
best_clf
The training F1 Score is 0.8148148148148148
The testing F1 Score is 0.8
DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=4,
max_features=None, max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=2, min_samples_split=2,
min_weight_fraction_leaf=0.0, presort=False,
random_state=42, splitter='best')
由此可以看出,最佳參數爲:
max_depth=4
min_samples_leaf=2
min_samples_split=2
且相對於第一個圖,邊界更爲簡單,這意味着它不太可能過擬合。
1.5 交叉驗證可視化
首先看一下不同參數下的信息:
results = pd.DataFrame(grid_obj.cv_results_)
results.T
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ... | 115 | 116 | 117 | 118 | 119 | 120 | 121 | 122 | 123 | 124 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mean_fit_time | 0.000536919 | 0.000609636 | 0.00067091 | 0.0005006 | 0.000532627 | 0.000538429 | 0.00162276 | 0.000725031 | 0.000346661 | 0.000960668 | ... | 0.000691652 | 0.000363668 | 0.00054733 | 0.000414769 | 0.000365416 | 0.000314713 | 0.000483354 | 0.000389099 | 0.000378688 | 0.000585318 |
std_fit_time | 7.36079e-05 | 0.000217965 | 0.000120917 | 7.64067e-05 | 0.000118579 | 0.000201879 | 0.00125017 | 0.000257437 | 2.95338e-05 | 0.000841452 | ... | 0.00027542 | 3.20732e-05 | 0.000166427 | 5.31612e-05 | 2.22742e-05 | 5.03509e-06 | 0.000156771 | 0.000113168 | 6.09452e-05 | 0.000168713 |
mean_score_time | 0.00124542 | 0.00209157 | 0.0011754 | 0.00118478 | 0.00127451 | 0.00132982 | 0.00173569 | 0.00158167 | 0.000804345 | 0.00165256 | ... | 0.00107495 | 0.000776132 | 0.0010496 | 0.00107972 | 0.000799974 | 0.000889381 | 0.00097998 | 0.000957966 | 0.00082167 | 0.00108504 |
std_score_time | 0.000460223 | 0.00131765 | 0.000217313 | 0.000175357 | 0.000274129 | 0.000684221 | 0.00012585 | 0.000531796 | 2.83336e-05 | 0.00103978 | ... | 0.000327278 | 1.61637e-05 | 0.000181963 | 0.000226213 | 3.18651e-05 | 0.00015253 | 0.000282182 | 0.00014771 | 5.40954e-05 | 0.00015636 |
param_max_depth | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ... | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |
param_min_samples_leaf | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ... | 8 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 10 | 10 |
param_min_samples_split | 2 | 4 | 6 | 8 | 10 | 2 | 4 | 6 | 8 | 10 | ... | 2 | 4 | 6 | 8 | 10 | 2 | 4 | 6 | 8 | 10 |
params | {'max_depth': 2, 'min_samples_leaf': 2, 'min_s... | {'max_depth': 2, 'min_samples_leaf': 2, 'min_s... | {'max_depth': 2, 'min_samples_leaf': 2, 'min_s... | {'max_depth': 2, 'min_samples_leaf': 2, 'min_s... | {'max_depth': 2, 'min_samples_leaf': 2, 'min_s... | {'max_depth': 2, 'min_samples_leaf': 4, 'min_s... | {'max_depth': 2, 'min_samples_leaf': 4, 'min_s... | {'max_depth': 2, 'min_samples_leaf': 4, 'min_s... | {'max_depth': 2, 'min_samples_leaf': 4, 'min_s... | {'max_depth': 2, 'min_samples_leaf': 4, 'min_s... | ... | {'max_depth': 10, 'min_samples_leaf': 8, 'min_... | {'max_depth': 10, 'min_samples_leaf': 8, 'min_... | {'max_depth': 10, 'min_samples_leaf': 8, 'min_... | {'max_depth': 10, 'min_samples_leaf': 8, 'min_... | {'max_depth': 10, 'min_samples_leaf': 8, 'min_... | {'max_depth': 10, 'min_samples_leaf': 10, 'min... | {'max_depth': 10, 'min_samples_leaf': 10, 'min... | {'max_depth': 10, 'min_samples_leaf': 10, 'min... | {'max_depth': 10, 'min_samples_leaf': 10, 'min... | {'max_depth': 10, 'min_samples_leaf': 10, 'min... |
split0_test_score | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 | ... | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 | 0.642857 |
split1_test_score | 0.764706 | 0.764706 | 0.764706 | 0.764706 | 0.764706 | 0.764706 | 0.764706 | 0.764706 | 0.764706 | 0.764706 | ... | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
split2_test_score | 0.709677 | 0.709677 | 0.709677 | 0.709677 | 0.709677 | 0.709677 | 0.709677 | 0.709677 | 0.709677 | 0.709677 | ... | 0.714286 | 0.714286 | 0.714286 | 0.714286 | 0.714286 | 0.666667 | 0.666667 | 0.666667 | 0.666667 | 0.666667 |
mean_test_score | 0.705698 | 0.705698 | 0.705698 | 0.705698 | 0.705698 | 0.705698 | 0.705698 | 0.705698 | 0.705698 | 0.705698 | ... | 0.617857 | 0.617857 | 0.617857 | 0.617857 | 0.617857 | 0.602381 | 0.602381 | 0.602381 | 0.602381 | 0.602381 |
std_test_score | 0.0501306 | 0.0501306 | 0.0501306 | 0.0501306 | 0.0501306 | 0.0501306 | 0.0501306 | 0.0501306 | 0.0501306 | 0.0501306 | ... | 0.0889995 | 0.0889995 | 0.0889995 | 0.0889995 | 0.0889995 | 0.0737135 | 0.0737135 | 0.0737135 | 0.0737135 | 0.0737135 |
rank_test_score | 14 | 14 | 14 | 14 | 14 | 14 | 14 | 14 | 14 | 14 | ... | 42 | 42 | 42 | 42 | 42 | 62 | 62 | 62 | 62 | 62 |
14 rows × 125 columns
接着我們來看一下在不同的最大深度(max_depth)下,每片葉子的最小樣本數(min_samples_leaf)和每次分裂的最小樣本數(min_samples_split)對決策樹模型的泛化性能的影響。
首先定義一個函數來繪製不同最大深度下的熱力圖(需安裝 mglearn):
def hotmap(max_depth, results):
fliter = results[results['param_max_depth']==max_depth]
scores = np.array(fliter['mean_test_score']).reshape(5, 5)
mglearn.tools.heatmap(scores, xlabel='min_samples_split', xticklabels=parameters['min_samples_split'],
ylabel='min_samples_leaf', yticklabels=parameters['min_samples_leaf'], cmap="viridis")
繪製到子圖中:
import matplotlib.pyplot as plt
plt.figure(figsize=(20, 20))
plt
for i in [1,2,3,4,5]:
plt.subplot(1,5,i, title='max_depth={}'.format(2*i))
hotmap(2*i, results)
從圖中可以看出,每次分裂的最小樣本數(min_samples_split)對模型幾乎沒有影響,而隨着最大深度(max_depth)的增加,模型得分逐漸降低。
1.5 總結
通過使用網格搜索,我們將 F1 分數從 0.7 提高到 0.8(同時我們失去了一些訓練分數,但這沒問題)。 另外,如果你看繪製的圖,第二個模型的邊界更爲簡單,這意味着它不太可能過擬合。