原理参考：
Python手写实现朴素贝叶斯（从原理到代码）
朴素贝叶斯算法的Python实现（多项式、高斯）
三种常用的朴素贝叶斯实现算法——高斯朴素贝叶斯、伯努利朴素贝叶斯、多项式朴素贝叶斯
- 伯努利模型
- 多项式模型
- 高斯模型
python实现：
import numpy as np
class NaiveBayes(object):
def __init__(self, alpha = 1.0, fit_prior=True):
self.alpha = alpha
self.fit_prior = fit_prior #是否学习类的先验几率，False则使用统一的先验
self.class_prior = None #类的先验几率，若指定则先验不能根据数据调整
self.classes = None
self.conditional_prob = None
self.predict_prob = None
def fit(self,x,y):
#计算类别y的先验几率
self.classes = np.unique(y)
if self.class_prior == None:#先验几率没有指定
class_num = len(self.classes)
self.class_prior = {}
if not self.fit_prior:
for d in self.classes:
self.class_prior[d] = 1.0/class_num
else:
for d in self.classes:
c_num = np.sum(np.equal(y,d))
self.class_prior[d]=(c_num+self.alpha) / (len(y) + class_num * self.alpha)
print(self.class_prior)
#计算条件几率------伯努利
self.conditional_prob = {}#{x1|y1:p1,x2|y1:p2,.....,x1|y2:p3,x2|y2:p4,.....}
x_class = [0,1]
y = list(y)
for yy in self.class_prior.keys():
y_index = [i for i,label in enumerate(y) if label == yy] #标签的先验几率
for i in range(len(x)):
for c in x_class:
x_index = [j for j,feature in enumerate(x[i]) if feature == c]
xy_count = len(set(x_index) & set(y_index))
pkey = str(c) + '|' + str(yy)
self.conditional_prob[pkey] = (xy_count+self.alpha) / (len(y_index)+2)
print(self.conditional_prob)
return self
def predict(self, x):
labels = []
for i in range(x.shape[0]):
self.predict_prob = {}
for j in self.classes:
self.predict_prob[j] = self.class_prior[j]
for d in x[i]:
self.predict_prob[j] = self.predict_prob[j]*self.conditional_prob[str(d) + '|'+ str(j)]
print(self.predict_prob)
label = max(self.predict_prob, key=self.predict_prob.get)
labels.append(label)
return labels
if __name__ == '__main__':
x = np.array([[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1],[0,1,1,0,0,0,1,1,1,1,1,1,1,1,1]])
y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
nb = NaiveBayes(alpha=1.0,fit_prior=True)
nb.fit(x, y)
print('预测值为：', nb.predict(np.array([[0,0]])))
python调包：
import numpy as np
from sklearn.naive_bayes import BernoulliNB
if __name__ == '__main__':
x = np.array([[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1],[0,1,1,0,0,0,1,1,1,1,1,1,1,1,1]]).T
y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
bnb = BernoulliNB()
bnb.fit(x,y)
print('预测值为：', bnb.predict(np.array([[0,0]])))
多项式模型
python实现：
import numpy as np
class MultinomialNB(object):
def __init__(self, alpha = 1.0, fit_prior=True):
self.alpha = alpha
self.fit_prior = fit_prior #是否学习类的先验几率，False则使用统一的先验
self.class_prior = None #类的先验几率，若指定则先验不能根据数据调整
self.classes = None
self.conditional_prob = None
self.predict_prob = None
def fit(self,x,y):
#计算类别y的先验几率
self.classes = np.unique(y)
if self.class_prior == None:#先验几率没有指定
class_num = len(self.classes)
self.class_prior = {}
if not self.fit_prior:
for d in self.classes:
self.class_prior[d] = 1.0/class_num
else:
for d in self.classes:
c_num = np.sum(np.equal(y,d))
self.class_prior[d]=(c_num+self.alpha) / (len(y) + class_num * self.alpha)
print(self.class_prior)
#计算条件几率------多项式
self.conditional_prob = {}#{x1|y1:p1,x2|y1:p2,.....,x1|y2:p3,x2|y2:p4,.....}
y = list(y)
for yy in self.class_prior.keys():
y_index = [i for i,label in enumerate(y) if label == yy] #标签的先验几率
for i in range(len(x)):
x_class = np.unique(x[i])
#print(x_class)
for c in list(x_class):
x_index = [j for j,feature in enumerate(x[i]) if feature == c]
xy_count = len(set(x_index) & set(y_index))
pkey = str(c) + '|' + str(yy)
self.conditional_prob[pkey] = (xy_count+self.alpha) / (len(y_index)+x_class.shape[0])
print(self.conditional_prob)
return self
def predict(self, x):
labels = []
for i in range(x.shape[0]):
self.predict_prob = {}
for j in self.classes:
self.predict_prob[j] = self.class_prior[j]
for d in x[i]:
self.predict_prob[j] = self.predict_prob[j]*self.conditional_prob[str(d) + '|'+ str(j)]
print(self.predict_prob)
label = max(self.predict_prob, key=self.predict_prob.get)
labels.append(label)
return labels
if __name__ == '__main__':
x = np.array([[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3],[1,2,2,1,1,1,2,2,3,3,3,2,2,3,3]])
y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
mnb = MultinomialNB(alpha=1.0,fit_prior=True)
mnb.fit(x, y)
print('预测值为：', mnb.predict(np.array([[2,1]])))
python调包：
import numpy as np
from sklearn.naive_bayes import MultinomialNB
if __name__ == '__main__':
x = np.array([[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3],[1,2,2,1,1,1,2,2,3,3,3,2,2,3,3]]).T
y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
bnb = MultinomialNB()
bnb.fit(x,y)
print('预测值为：', bnb.predict(np.array([[2,1]])))
高斯模型
python实现：
import numpy as np
class GaussionNB(object): #计算条件几率的方法不同
def __init__(self, fit_prior=True):
self.fit_prior = fit_prior #是否学习类的先验几率，False则使用统一的先验
self.class_prior = None #类的先验几率，若指定则先验不能根据数据调整
self.classes = None
self.mean = None
self.var = None
self.predict_prob = None
def fit(self,x,y):
#计算类别y的先验几率
self.classes = np.unique(y)
if self.class_prior == None:#先验几率没有指定
class_num = len(self.classes)
self.class_prior = {}
if not self.fit_prior:
for d in self.classes:
self.class_prior[d] = 1.0/class_num
else:
self.class_prior = {}
for d in self.classes:
c_num = np.sum(np.equal(y,d))
self.class_prior[d]= c_num / len(y)
print(self.class_prior)
#计算条件几率------高斯模型
self.mean = {}
self.var = {}
y = list(y)
for yy in self.class_prior.keys():
y_index = [i for i,label in enumerate(y) if label == yy] #标签的先验几率
#print(y_index)
for i in range(len(x)):
x_class =[]
for j in y_index:
x_class.append(x[i][j])
pkey = str(i) + '|' + str(yy)
mean = np.mean(x_class)
var = np.var(x_class)
self.mean[pkey] = mean
self.var[pkey] = var
#print(x_class)
print(self.mean, self.var)
return self
def _calculat_prob_gaussion(self,mu,sigma,x):
return 1.0/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (x - mu)**2 / (2 * sigma**2))
def predict(self,x):
labels = []
for i in range(x.shape[0]):
self.predict_prob = {}
for yy in self.class_prior.keys():
self.predict_prob[yy] = self.class_prior[yy]
for c,d in enumerate(list(x[i])):
tkey = str(c)+'|'+str(yy)
mu = self.mean[tkey]
sigma = self.var[tkey]
print(mu,sigma)
self.predict_prob[yy] = self.predict_prob[yy]*self._calculat_prob_gaussion(mu,sigma,d)
print(self.predict_prob)
label = max(self.predict_prob, key=self.predict_prob.get)
labels.append(label)
return labels
if __name__ == '__main__':
x = np.array([[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3],[1,2,2,1,1,1,2,2,3,3,3,2,2,3,3]])
y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
gnb = GaussionNB()
gnb.fit(x, y)
print('预测值为：', gnb.predict(np.array([[2,1]])))
python调包：
import numpy as np
from sklearn.naive_bayes import GaussianNB
if __name__ == '__main__':
x = np.array([[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3],[1,2,2,1,1,1,2,2,3,3,3,2,2,3,3]]).T
y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
gnb = GaussianNB()
gnb.fit(x,y)
print('预测值为：', gnb.predict(np.array([[2,1]])))
