1 理論
樸素貝葉斯是生成學習方法,即訓練數據學習聯合概率分佈 ,然後求得後驗概率分佈,利用貝葉斯定理與學到的聯合概率模型進行分類預測,公式如下:
2 代碼
import numpy as np
import pandas as pd
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from collections import Counter
import math
def create_data():
iris = load_iris()
df = pd.DataFrame(iris.data, columns=iris.feature_names)
df['label'] = iris.target
df.columns = ['sepal length', 'sepal width', 'petal length', 'petal width', 'label']
data = np.array(df.iloc[:100, :])
return data[:,:-1], data[:,-1]
# 創建NB類
class NaiveBayes:
def __init__(self):
self.model = None
# 數學期望
def mean(X):
return sum(X) / float(len(X))
# 標準差
def stdev(self, X):
avg = self.mean(X)
return math.sqrt(sum([pow(x - avg, 2) for x in X]) / float(len(X)))
# 概率密度函數
def gaussian_probability(self, x, mean, stdev):
exponent = math.exp(-(math.pow(x - mean, 2) /
(2 * math.pow(stdev, 2))))
return (1 / (math.sqrt(2 * math.pi) * stdev)) * exponent
# 處理X_train
def summarize(self, train_data):
summaries = [(self.mean(i), self.stdev(i)) for i in zip(*train_data)]
return summaries
# 分類別求出數學期望和標準差
def fit(self, X, y):
labels = list(set(y))
data = {label: [] for label in labels}
for f, label in zip(X, y):
data[label].append(f)
self.model = {
label: self.summarize(value)
for label, value in data.items()
}
return 'gaussianNB train done!'
# 計算概率
def calculate_probabilities(self, input_data):
probabilities = {}
for label, value in self.model.items():
probabilities[label] = 1
for i in range(len(value)):
mean, stdev = value[i]
probabilities[label] *= self.gaussian_probability(
input_data[i], mean, stdev)
return probabilities
# 類別
def predict(self, X_test):
label = sorted(
self.calculate_probabilities(X_test).items(),
key=lambda x: x[-1])[-1][0]
return label
# 置信度
def score(self, X_test, y_test):
right = 0
for X, y in zip(X_test, y_test):
label = self.predict(X)
if label == y:
right += 1
return right / float(len(X_test))
if __name__ == '__main__':
X, y = create_data()
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)
model = NaiveBayes()
model.fit(X_train, y_train)
model.score(X_test, y_test)
3 參考
理論:周志華《機器學習》,李航《統計學習方法》
代碼:https://github.com/fengdu78/lihang-code