python實現隨機森林random forest的原理及方法

想通過隨機森林來獲取數據的主要特征
1、理論
隨機森林是一個高度靈活的機器學習方法，擁有廣泛的應用前景，從市場營銷到醫療保健保險。 既可以用來做市場營銷模擬的建模，統計客戶來源，保留和流失。也可用來預測疾病的風險和病患者的易感性。
根據個體學習器的生成方式，目前的集成學習方法大致可分為兩大類，即個體學習器之間存在強依賴關系，必須串行生成的序列化方法，以及個體學習器間不存在強依賴關系，可同時生成的并行化方法；
前者的代表是Boosting，后者的代表是Bagging和“隨機森林”（Random
Forest）
隨機森林在以決策樹為基學習器構建Bagging集成的基礎上，進一步在決策樹的訓練過程中引入了隨機屬性選擇（即引入隨機特征選擇）。
簡單來說，隨機森林就是對決策樹的集成，但有兩點不同：
（2）特征選取的差異性：每個決策樹的n個分類特征是在所有特征中隨機選擇的（n是一個需要我們自己調整的參數）
隨機森林，簡單理解， 比如預測salary，就是構建多個決策樹job，age，house，然后根據要預測的量的各個特征（teacher，39，suburb）分別在對應決策樹的目標值概率（salary<5000,salary>=5000），從而，確定預測量的發生概率（如，預測出P(salary<5000)=0.3）.
隨機森林是一個可做能夠回歸和分類。 它具備處理大數據的特性，而且它有助于估計或變量是非常重要的基礎數據建模。
參數說明：
最主要的兩個參數是n_estimators和max_features。
n_estimators：表示森林里樹的個數。理論上是越大越好。但是伴隨著就是計算時間的增長。但是并不是取得越大就會越好，預測效果最好的將會出現在合理的樹個數。
max_features：隨機選擇特征集合的子集合，并用來分割節點。子集合的個數越少，方差就會減少的越快，但同時偏差就會增加的越快。根據較好的實踐經驗。如果是回歸問題則：

max_features＝n_features，如果是分類問題則max_features＝sqrt(n_features)。

如果想獲取較好的結果，必須將max_depth＝None,同時min_sample_split=1。
同時還要記得進行cross_validated（交叉驗證），除此之外記得在random forest中，bootstrap=True。但在extra-trees中，bootstrap=False。

2、隨機森林python實現

2.1Demo1

實現隨機森林基本功能    
#隨機森林
from sklearn.tree import DecisionTreeRegressor
from sklearn.ensemble import RandomForestRegressor
import numpy as np
 
from sklearn.datasets import load_iris
iris=load_iris()
#print iris#iris的４個屬性是：萼片寬度　萼片長度　花瓣寬度　花瓣長度　標簽是花的種類：setosa versicolour virginica
print(iris['target'].shape)
rf=RandomForestRegressor()#這里使用了默認的參數設置
rf.fit(iris.data[:150],iris.target[:150])#進行模型的訓練
 
#隨機挑選兩個預測不相同的樣本
instance=iris.data[[100,109]]
print(instance)
rf.predict(instance[[0]])
print('instance 0 prediction；',rf.predict(instance[[0]]))
print( 'instance 1 prediction；',rf.predict(instance[[1]]))
print(iris.target[100],iris.target[109])

運行結果

(150,)
[[ 6.3  3.3  6.   2.5]
 [ 7.2  3.6  6.1  2.5]]
instance 0 prediction； [ 2.]
instance 1 prediction； [ 2.]
2 2

2.2 Demo2

3種方法的比較    
#random forest test
from sklearn.model_selection import cross_val_score
from sklearn.datasets import make_blobs
from sklearn.ensemble import RandomForestClassifier
from sklearn.ensemble import ExtraTreesClassifier
from sklearn.tree import DecisionTreeClassifier
X, y = make_blobs(n_samples=10000, n_features=10, centers=100,random_state=0)
 
clf = DecisionTreeClassifier(max_depth=None, min_samples_split=2,random_state=0)
scores = cross_val_score(clf, X, y)
print(scores.mean())    
 
 
clf = RandomForestClassifier(n_estimators=10, max_depth=None,min_samples_split=2, random_state=0)
scores = cross_val_score(clf, X, y)
print(scores.mean())    
 
clf = ExtraTreesClassifier(n_estimators=10, max_depth=None,min_samples_split=2, random_state=0)
scores = cross_val_score(clf, X, y)
print(scores.mean())

運行結果：

0.979408793821
0.999607843137
0.999898989899

2.3 Demo3-實現特征選擇
#隨機森林2
from sklearn.tree import DecisionTreeRegressor
from sklearn.ensemble import RandomForestRegressor
import numpy as np
from sklearn.datasets import load_iris
iris=load_iris()
 
from sklearn.model_selection import cross_val_score, ShuffleSplit
X = iris["data"]
Y = iris["target"]
names = iris["feature_names"]
rf = RandomForestRegressor()
scores = []
for i in range(X.shape[1]):
 score = cross_val_score(rf, X[:, i:i+1], Y, scoring="r2",
    cv=ShuffleSplit(len(X), 3, .3))
 scores.append((round(np.mean(score), 3), names[i]))
print(sorted(scores, reverse=True))
運行結果：
[(0.89300000000000002, 'petal width (cm)'), (0.82099999999999995, 'petal length
(cm)'), (0.13, 'sepal length (cm)'), (-0.79100000000000004, 'sepal width (cm)')]
2.4 demo4-隨機森林
本來想利用以下代碼來構建隨機隨機森林決策樹，但是，遇到的問題是，程序一直在運行，無法響應，還需要調試。    
#隨機森林4
#coding:utf-8
import csv
from random import seed
from random import randrange
from math import sqrt
def loadCSV(filename):#加載數據，一行行的存入列表
 dataSet = []
 with open(filename, 'r') as file:
 csvReader = csv.reader(file)
 for line in csvReader:
  dataSet.append(line)
 return dataSet
 
# 除了標簽列，其他列都轉換為float類型
def column_to_float(dataSet):
 featLen = len(dataSet[0]) - 1
 for data in dataSet:
 for column in range(featLen):
  data[column] = float(data[column].strip())
 
# 將數據集隨機分成N塊，方便交叉驗證，其中一塊是測試集，其他四塊是訓練集
def spiltDataSet(dataSet, n_folds):
 fold_size = int(len(dataSet) / n_folds)
 dataSet_copy = list(dataSet)
 dataSet_spilt = []
 for i in range(n_folds):
 fold = []
 while len(fold) < fold_size: # 這里不能用if，if只是在第一次判斷時起作用，while執行循環，直到條件不成立
  index = randrange(len(dataSet_copy))
  fold.append(dataSet_copy.pop(index)) # pop() 函數用于移除列表中的一個元素（默認最后一個元素），并且返回該元素的值。
 dataSet_spilt.append(fold)
 return dataSet_spilt
 
# 構造數據子集
def get_subsample(dataSet, ratio):
 subdataSet = []
 lenSubdata = round(len(dataSet) * ratio)#返回浮點數
 while len(subdataSet) < lenSubdata:
 index = randrange(len(dataSet) - 1)
 subdataSet.append(dataSet[index])
 # print len(subdataSet)
 return subdataSet
 
# 分割數據集
def data_spilt(dataSet, index, value):
 left = []
 right = []
 for row in dataSet:
 if row[index] < value:
  left.append(row)
 else:
  right.append(row)
 return left, right
 
# 計算分割代價
def spilt_loss(left, right, class_values):
 loss = 0.0
 for class_value in class_values:
 left_size = len(left)
 if left_size != 0: # 防止除數為零
  prop = [row[-1] for row in left].count(class_value) / float(left_size)
  loss += (prop * (1.0 - prop))
 right_size = len(right)
 if right_size != 0:
  prop = [row[-1] for row in right].count(class_value) / float(right_size)
  loss += (prop * (1.0 - prop))
 return loss
 
# 選取任意的n個特征，在這n個特征中，選取分割時的最優特征
def get_best_spilt(dataSet, n_features):
 features = []
 class_values = list(set(row[-1] for row in dataSet))
 b_index, b_value, b_loss, b_left, b_right = 999, 999, 999, None, None
 while len(features) < n_features:
 index = randrange(len(dataSet[0]) - 1)
 if index not in features:
  features.append(index)
 # print 'features:',features
 for index in features:#找到列的最適合做節點的索引，（損失最?。?
 for row in dataSet:
  left, right = data_spilt(dataSet, index, row[index])#以它為節點的，左右分支
  loss = spilt_loss(left, right, class_values)
  if loss < b_loss:#尋找最小分割代價
  b_index, b_value, b_loss, b_left, b_right = index, row[index], loss, left, right
 # print b_loss
 # print type(b_index)
 return {'index': b_index, 'value': b_value, 'left': b_left, 'right': b_right}
 
# 決定輸出標簽
def decide_label(data):
 output = [row[-1] for row in data]
 return max(set(output), key=output.count)
 
# 子分割，不斷地構建葉節點的過程對對對
def sub_spilt(root, n_features, max_depth, min_size, depth):
 left = root['left']
 # print left
 right = root['right']
 del (root['left'])
 del (root['right'])
 # print depth
 if not left or not right:
 root['left'] = root['right'] = decide_label(left + right)
 # print 'testing'
 return
 if depth > max_depth:
 root['left'] = decide_label(left)
 root['right'] = decide_label(right)
 return
 if len(left) < min_size:
 root['left'] = decide_label(left)
 else:
 root['left'] = get_best_spilt(left, n_features)
 # print 'testing_left'
 sub_spilt(root['left'], n_features, max_depth, min_size, depth + 1)
 if len(right) < min_size:
 root['right'] = decide_label(right)
 else:
 root['right'] = get_best_spilt(right, n_features)
 # print 'testing_right'
 sub_spilt(root['right'], n_features, max_depth, min_size, depth + 1)
 
 # 構造決策樹
def build_tree(dataSet, n_features, max_depth, min_size):
 root = get_best_spilt(dataSet, n_features)
 sub_spilt(root, n_features, max_depth, min_size, 1)
 return root
# 預測測試集結果
def predict(tree, row):
 predictions = []
 if row[tree['index']] < tree['value']:
 if isinstance(tree['left'], dict):
  return predict(tree['left'], row)
 else:
  return tree['left']
 else:
 if isinstance(tree['right'], dict):
  return predict(tree['right'], row)
 else:
  return tree['right']
  # predictions=set(predictions)
def bagging_predict(trees, row):
 predictions = [predict(tree, row) for tree in trees]
 return max(set(predictions), key=predictions.count)
# 創建隨機森林
def random_forest(train, test, ratio, n_feature, max_depth, min_size, n_trees):
 trees = []
 for i in range(n_trees):
 train = get_subsample(train, ratio)#從切割的數據集中選取子集
 tree = build_tree(train, n_features, max_depth, min_size)
 # print 'tree %d: '%i,tree
 trees.append(tree)
 # predict_values = [predict(trees,row) for row in test]
 predict_values = [bagging_predict(trees, row) for row in test]
 return predict_values
# 計算準確率
def accuracy(predict_values, actual):
 correct = 0
 for i in range(len(actual)):
 if actual[i] == predict_values[i]:
  correct += 1
 return correct / float(len(actual))
if __name__ == '__main__':
 seed(1)
 dataSet = loadCSV(r'G:\0研究生\tianchiCompetition\訓練小樣本2.csv')
 column_to_float(dataSet)
 n_folds = 5
 max_depth = 15
 min_size = 1
 ratio = 1.0
 # n_features=sqrt(len(dataSet)-1)
 n_features = 15
 n_trees = 10
 folds = spiltDataSet(dataSet, n_folds)#先是切割數據集
 scores = []
 for fold in folds:
 train_set = folds[
   :] # 此處不能簡單地用train_set=folds，這樣用屬于引用,那么當train_set的值改變的時候，folds的值也會改變，所以要用復制的形式。（L[:]）能夠復制序列，D.copy() 能夠復制字典，list能夠生成拷貝 list(L)
 train_set.remove(fold)#選好訓練集
 # print len(folds)
 train_set = sum(train_set, []) # 將多個fold列表組合成一個train_set列表
 # print len(train_set)
 test_set = []
 for row in fold:
  row_copy = list(row)
  row_copy[-1] = None
  test_set.append(row_copy)
  # for row in test_set:
  # print row[-1]
 actual = [row[-1] for row in fold]
 predict_values = random_forest(train_set, test_set, ratio, n_features, max_depth, min_size, n_trees)
 accur = accuracy(predict_values, actual)
 scores.append(accur)
 print ('Trees is %d' % n_trees)
 print ('scores:%s' % scores)
 print ('mean score:%s' % (sum(scores) / float(len(scores))))

2.5 隨機森林分類sonic data    
# CART on the Bank Note dataset
from random import seed
from random import randrange
from csv import reader
 
# Load a CSV file
def load_csv(filename):
 file = open(filename, "r")
 lines = reader(file)
 dataset = list(lines)
 return dataset
 
# Convert string column to float
def str_column_to_float(dataset, column):
 for row in dataset:
 row[column] = float(row[column].strip())
 
# Split a dataset into k folds
def cross_validation_split(dataset, n_folds):
 dataset_split = list()
 dataset_copy = list(dataset)
 fold_size = int(len(dataset) / n_folds)
 for i in range(n_folds):
 fold = list()
 while len(fold) < fold_size:
  index = randrange(len(dataset_copy))
  fold.append(dataset_copy.pop(index))
 dataset_split.append(fold)
 return dataset_split
 
# Calculate accuracy percentage
def accuracy_metric(actual, predicted):
 correct = 0
 for i in range(len(actual)):
 if actual[i] == predicted[i]:
  correct += 1
 return correct / float(len(actual)) * 100.0
 
# Evaluate an algorithm using a cross validation split
def evaluate_algorithm(dataset, algorithm, n_folds, *args):
 folds = cross_validation_split(dataset, n_folds)
 scores = list()
 for fold in folds:
 train_set = list(folds)
 train_set.remove(fold)
 train_set = sum(train_set, [])
 test_set = list()
 for row in fold:
  row_copy = list(row)
  test_set.append(row_copy)
  row_copy[-1] = None
 predicted = algorithm(train_set, test_set, *args)
 actual = [row[-1] for row in fold]
 accuracy = accuracy_metric(actual, predicted)
 scores.append(accuracy)
 return scores
 
# Split a data set based on an attribute and an attribute value
def test_split(index, value, dataset):
 left, right = list(), list()
 for row in dataset:
 if row[index] < value:
  left.append(row)
 else:
  right.append(row)
 return left, right
 
# Calculate the Gini index for a split dataset
def gini_index(groups, class_values):
 gini = 0.0
 for class_value in class_values:
 for group in groups:
  size = len(group)
  if size == 0:
  continue
  proportion = [row[-1] for row in group].count(class_value) / float(size)
  gini += (proportion * (1.0 - proportion))
 return gini
 
# Select the best split point for a dataset
def get_split(dataset):
 class_values = list(set(row[-1] for row in dataset))
 b_index, b_value, b_score, b_groups = 999, 999, 999, None
 for index in range(len(dataset[0])-1):
 for row in dataset:
  groups = test_split(index, row[index], dataset)
  gini = gini_index(groups, class_values)
  if gini < b_score:
  b_index, b_value, b_score, b_groups = index, row[index], gini, groups
 print ({'index':b_index, 'value':b_value})
 return {'index':b_index, 'value':b_value, 'groups':b_groups}
 
# Create a terminal node value
def to_terminal(group):
 outcomes = [row[-1] for row in group]
 return max(set(outcomes), key=outcomes.count)
 
# Create child splits for a node or make terminal
def split(node, max_depth, min_size, depth):
 left, right = node['groups']
 del(node['groups'])
 # check for a no split
 if not left or not right:
 node['left'] = node['right'] = to_terminal(left + right)
 return
 # check for max depth
 if depth >= max_depth:
 node['left'], node['right'] = to_terminal(left), to_terminal(right)
 return
 # process left child
 if len(left) <= min_size:
 node['left'] = to_terminal(left)
 else:
 node['left'] = get_split(left)
 split(node['left'], max_depth, min_size, depth+1)
 # process right child
 if len(right) <= min_size:
 node['right'] = to_terminal(right)
 else:
 node['right'] = get_split(right)
 split(node['right'], max_depth, min_size, depth+1)
 
# Build a decision tree
def build_tree(train, max_depth, min_size):
 root = get_split(train)
 split(root, max_depth, min_size, 1)
 return root
 
# Make a prediction with a decision tree
def predict(node, row):
 if row[node['index']] < node['value']:
 if isinstance(node['left'], dict):
  return predict(node['left'], row)
 else:
  return node['left']
 else:
 if isinstance(node['right'], dict):
  return predict(node['right'], row)
 else:
  return node['right']
 
# Classification and Regression Tree Algorithm
def decision_tree(train, test, max_depth, min_size):
 tree = build_tree(train, max_depth, min_size)
 predictions = list()
 for row in test:
 prediction = predict(tree, row)
 predictions.append(prediction)
 return(predictions)
 
# Test CART on Bank Note dataset
seed(1)
# load and prepare data
filename = r'G:\0pythonstudy\決策樹\sonar.all-data.csv'
dataset = load_csv(filename)
# convert string attributes to integers
for i in range(len(dataset[0])-1):
 str_column_to_float(dataset, i)
# evaluate algorithm
n_folds = 5
max_depth = 5
min_size = 10
scores = evaluate_algorithm(dataset, decision_tree, n_folds, max_depth, min_size)
print('Scores: %s' % scores)
print('Mean Accuracy: %.3f%%' % (sum(scores)/float(len(scores))))

運行結果：

{'index': 38, 'value': 0.0894}
{'index': 36, 'value': 0.8459}
{'index': 50, 'value': 0.0024}
{'index': 15, 'value': 0.0906}
{'index': 16, 'value': 0.9819}
{'index': 10, 'value': 0.0785}
{'index': 16, 'value': 0.0886}
{'index': 38, 'value': 0.0621}
{'index': 5, 'value': 0.0226}
{'index': 8, 'value': 0.0368}
{'index': 11, 'value': 0.0754}
{'index': 0, 'value': 0.0239}
{'index': 8, 'value': 0.0368}
{'index': 29, 'value': 0.1671}
{'index': 46, 'value': 0.0237}
{'index': 38, 'value': 0.0621}
{'index': 14, 'value': 0.0668}
{'index': 4, 'value': 0.0167}
{'index': 37, 'value': 0.0836}
{'index': 12, 'value': 0.0616}
{'index': 7, 'value': 0.0333}
{'index': 33, 'value': 0.8741}
{'index': 16, 'value': 0.0886}
{'index': 8, 'value': 0.0368}
{'index': 33, 'value': 0.0798}
{'index': 44, 'value': 0.0298}
Scores: [48.78048780487805, 70.73170731707317, 58.536585365853654, 51.2195121951
2195, 39.02439024390244]
Mean Accuracy: 53.659%
請按任意鍵繼續. . .

知識點：
1.load CSV file    
from csv import reader
# Load a CSV file
def load_csv(filename):
 file = open(filename, "r")
 lines = reader(file)
 dataset = list(lines)
 return dataset
filename = r'G:\0pythonstudy\決策樹\sonar.all-data.csv'
dataset=load_csv(filename)
print(dataset)

2.把數據轉化成float格式    
# Convert string column to float
def str_column_to_float(dataset, column):
 for row in dataset:
 row[column] = float(row[column].strip())
 # print(row[column])
# convert string attributes to integers
for i in range(len(dataset[0])-1):
 str_column_to_float(dataset, i)

3.把最后一列的分類字符串轉化成0、1整數    
def str_column_to_int(dataset, column):
 class_values = [row[column] for row in dataset]#生成一個class label的list
 # print(class_values)
 unique = set(class_values)#set 獲得list的不同元素
 print(unique)
 lookup = dict()#定義一個字典
 # print(enumerate(unique))
 for i, value in enumerate(unique):
 lookup[value] = i
 # print(lookup)
 for row in dataset:
 row[column] = lookup[row[column]]
 print(lookup['M'])

4、把數據集分割成K份    
# Split a dataset into k folds
def cross_validation_split(dataset, n_folds):
 dataset_split = list()#生成空列表
 dataset_copy = list(dataset)
 print(len(dataset_copy))
 print(len(dataset))
 #print(dataset_copy)
 fold_size = int(len(dataset) / n_folds)
 for i in range(n_folds):
 fold = list()
 while len(fold) < fold_size:
  index = randrange(len(dataset_copy))
  # print(index)
  fold.append(dataset_copy.pop(index))#使用.pop()把里邊的元素都刪除（相當于轉移），這k份元素各不相同。
 dataset_split.append(fold)
 return dataset_split
n_folds=5
folds = cross_validation_split(dataset, n_folds)#k份元素各不相同的訓練集

5.計算正確率    
# Calculate accuracy percentage
def accuracy_metric(actual, predicted):
 correct = 0
 for i in range(len(actual)):
 if actual[i] == predicted[i]:
  correct += 1
 return correct / float(len(actual)) * 100.0#這個是二值分類正確性的表達式

6.二分類每列    
# Split a data set based on an attribute and an attribute value
def test_split(index, value, dataset):
 left, right = list(), list()#初始化兩個空列表
 for row in dataset:
 if row[index] < value:
  left.append(row)
 else:
  right.append(row)
 return left, right #返回兩個列表，每個列表以value為界限對指定行（index）進行二分類。

7.使用gini系數來獲得最佳分割點    
# Calculate the Gini index for a split dataset
def gini_index(groups, class_values):
 gini = 0.0
 for class_value in class_values:
 for group in groups:
  size = len(group)
  if size == 0:
  continue
  proportion = [row[-1] for row in group].count(class_value) / float(size)
  gini += (proportion * (1.0 - proportion))
 return gini
 
# Select the best split point for a dataset
def get_split(dataset):
 class_values = list(set(row[-1] for row in dataset))
 b_index, b_value, b_score, b_groups = 999, 999, 999, None
 for index in range(len(dataset[0])-1):
 for row in dataset:
  groups = test_split(index, row[index], dataset)
  gini = gini_index(groups, class_values)
  if gini < b_score:
  b_index, b_value, b_score, b_groups = index, row[index], gini, groups
 # print(groups)
 print ({'index':b_index, 'value':b_value,'score':gini})
 return {'index':b_index, 'value':b_value, 'groups':b_groups}

這段代碼，在求gini指數，直接應用定義式，不難理解。獲得最佳分割點可能比較難看懂，這里用了兩層迭代，一層是對不同列的迭代，一層是對不同行的迭代。并且，每次迭代，都對gini系數進行更新。

8、決策樹生成    
# Create child splits for a node or make terminal
def split(node, max_depth, min_size, depth):
 left, right = node['groups']
 del(node['groups'])
 # check for a no split
 if not left or not right:
 node['left'] = node['right'] = to_terminal(left + right)
 return
 # check for max depth
 if depth >= max_depth:
 node['left'], node['right'] = to_terminal(left), to_terminal(right)
 return
 # process left child
 if len(left) <= min_size:
 node['left'] = to_terminal(left)
 else:
 node['left'] = get_split(left)
 split(node['left'], max_depth, min_size, depth+1)
 # process right child
 if len(right) <= min_size:
 node['right'] = to_terminal(right)
 else:
 node['right'] = get_split(right)
 split(node['right'], max_depth, min_size, depth+1)

這里使用了遞歸編程，不斷生成左叉樹和右叉樹。

9.構建決策樹    
# Build a decision tree
def build_tree(train, max_depth, min_size):
 root = get_split(train)
 split(root, max_depth, min_size, 1)
 return root
tree=build_tree(train_set, max_depth, min_size)
print(tree)

10、預測test集    
# Build a decision tree
def build_tree(train, max_depth, min_size):
 root = get_split(train)#獲得最好的分割點,下標值，groups
 split(root, max_depth, min_size, 1)
 return root
# tree=build_tree(train_set, max_depth, min_size)
# print(tree)
 
# Make a prediction with a decision tree
def predict(node, row):
 print(row[node['index']])
 print(node['value'])
 if row[node['index']] < node['value']:#用測試集來代入訓練的最好分割點，分割點有偏差時，通過搜索左右叉樹來進一步比較。
 if isinstance(node['left'], dict):#如果是字典類型，執行操作
  return predict(node['left'], row)
 else:
  return node['left']
 else:
 if isinstance(node['right'], dict):
  return predict(node['right'], row)
 else:
  return node['right']
tree = build_tree(train_set, max_depth, min_size)
predictions = list()
for row in test_set:
 prediction = predict(tree, row)
 predictions.append(prediction)

11.評價決策樹    
# Evaluate an algorithm using a cross validation split
def evaluate_algorithm(dataset, algorithm, n_folds, *args):
 folds = cross_validation_split(dataset, n_folds)
 scores = list()
 for fold in folds:
 train_set = list(folds)
 train_set.remove(fold)
 train_set = sum(train_set, [])
 test_set = list()
 for row in fold:
  row_copy = list(row)
  test_set.append(row_copy)
  row_copy[-1] = None
 predicted = algorithm(train_set, test_set, *args)
 actual = [row[-1] for row in fold]
 accuracy = accuracy_metric(actual, predicted)
 scores.append(accuracy)
 return scores
以上就是本文的全部內容，希望對大家的學習有所幫助