贝叶斯推断|朴素贝叶斯分类|贝叶斯定理

近期，由于项目需求，需要用到贝叶斯定理及其相关知识，于是又系统的学习了一下，顺便做一下笔记。

参考资料：

• 概率论与数理统计的基础知识，这个PPT讲得非常通俗易懂，复习大学学过的知识
• 算法杂货铺——分类算法之朴素贝叶斯分类(Naive Bayesian classification) 理论讲的非常详细清楚
• 朴素贝叶斯的学习与分类 讲的非常精炼，代码用python实现得比较好

代码（非常详细的注释）：

#-*- coding:utf-8 -*-
import copy #用于深度拷贝，适用于复杂的数据结构
#复杂的数据结构看不懂，一定要在纸上画图，画出来就一目了然了

class native_bayes:

    def __init__(self, character_vec_, class_vec_):
        """
        # 缩进必须正确，不然会报错
        构造函数，传入的参数请看最底下的函数调用
        character_vec_：[("character_A",["A1","A2","A3"]), ("character_B",["B1","B2","B3"])] 是一个嵌套数据结构，最外层是一个列表，内层是元组，元组里还有列表
        class_vec_：["class_X", "class_Y"]
        """
        character_condition_per = {} #创建一个数据结构，建议在纸上画出结构图
        #这是一个嵌套的三层字典，用于统计计数
        for character_name in character_vec_:
            character_condition_per[character_name[0]] = {}
            for character_value in character_name[1]:
                character_condition_per[character_name[0]][character_value] = {
                    'num':0, # 记录该类别下该特征值在训练样本中的数量
                    'condition_per':0.0 # 记录该类别下各个特征值的条件概率
                }
        self.class_set = {} # 记录该类别下各个特征值的条件概率
        #这是一个两层字典，内嵌一个三层字典
        for class_name in class_vec_:
            self.class_set[class_name] = {
                'num':0, # 记录该类别在训练样本中的数量
                'class_per':0.0, # 记录该类别在训练样本中的先验概率
                'character_condition_per':copy.deepcopy(character_condition_per) #将上面的三层字典全部嵌套过来了
            }
        #print("init", character_vec_, self.class_set) #for debug
            
    def learn(self, sample_):
        """
        learn是训练函数，传入的参数为sample_：
        [
            {
                'character'  : {'character_A':'A1'}, #特征向量
                'class_name' : 'class_X'             #类别名称
            }
        ]
        """
        for each_sample in sample_:
            character_vec_ = each_sample['character']
            class_name = each_sample['class_name']
            data_for_class = self.class_set[class_name]
            data_for_class['num'] += 1
            
            # 各个特质值样本数量加1
            for character_name in character_vec_: #默认迭代的字典的键
                character_value =  character_vec_[character_name]
                data_for_character = data_for_class['character_condition_per'][character_name][character_value]
                data_for_character['num'] += 1
        
        # 数量计算完毕， 计算最终的概率值        
        sample_num = len(sample_)
        for each_sample in sample_:
            character_vec_ = each_sample['character']
            class_name = each_sample['class_name']
            data_for_class = self.class_set[class_name]
            # 计算类别的先验概率
            data_for_class['class_per'] = float(data_for_class['num'])/sample_num
            
            # 各个特质值的条件概率
            for character_name in character_vec_:
                character_value = character_vec_[character_name]
                data_for_character = data_for_class['character_condition_per'][character_name][character_value]
                data_for_character['condition_per'] = float(data_for_character['num'] / data_for_class['num'])
        # from pprint import pprint
        # pprint(self.class_set)  #for debug
        
    def classify(self, input_):
        """
        分类函数：输入参数input_：
        {
            "character_A":"A1",
            "character_B":"B3",
        }
        """
        best_class = ''
        max_per = 0.0
        for class_name in self.class_set:
            class_data = self.class_set[class_name]
            per = class_data['class_per']
            # 计算各个特征值条件概率的乘积
            for character_name in input_:
                character_per_data = class_data['character_condition_per'][character_name]
                per = per * character_per_data[input_[character_name]]['condition_per']
            print (class_name, per)
            if per >=max_per:
                best_class = class_name
              
        return best_class
                

#命名规则：函数参数后面加_，正常的则不加，非常容易区分    
#台头
character_vec = [("character_A",["A1","A2","A3"]),("character_B",["B1","B2","B3"])]
class_vec = ["class_X","class_Y"]

bayes = native_bayes(character_vec, class_vec)        #创建对象

sample = [  #创建训练集
            {
                'character'  : {'character_A':'A1', 'character_B':'B1'}, #特征向量
                'class_name' : 'class_X'             #类别名称
            },
            {
                'character'  : {'character_A':'A3', 'character_B':'B1'}, #特征向量
                'class_name' : 'class_X'             #类别名称
            },
            {
                'character'  : {'character_A':'A3', 'character_B':'B3'}, #特征向量
                'class_name' : 'class_X'             #类别名称
            },
            {
                'character'  : {'character_A':'A2', 'character_B':'B2'}, #特征向量
                'class_name' : 'class_X'             #类别名称
            },
            {
                'character'  : {'character_A':'A2', 'character_B':'B2'}, #特征向量
                'class_name' : 'class_Y'             #类别名称
            },
            {
                'character'  : {'character_A':'A3', 'character_B':'B1'}, #特征向量
                'class_name' : 'class_Y'             #类别名称
            },
            {
                'character'  : {'character_A':'A1', 'character_B':'B3'}, #特征向量
                'class_name' : 'class_Y'             #类别名称
            },
            {
                'character'  : {'character_A':'A1', 'character_B':'B3'}, #特征向量
                'class_name' : 'class_Y'             #类别名称
            },
            
        ]

input_data = { # 测试集
    "character_A":"A1",
    "character_B":"B3"
}

bayes.learn(sample) #学习
print(bayes.classify(input_data)) #测试