乍看起來似乎是要求一個(gè)概率，還要先得到額外三個(gè)概率，有用么？其實(shí)這個(gè)簡單的公式非常貼切人類推理的邏輯，即通過可以觀測的數(shù)據(jù)，推測不可觀測的數(shù)據(jù)。舉個(gè)例子，也許你在辦公室內(nèi)不知道外面天氣是晴天雨天，但是你觀測到有同事帶了雨傘，那么可以推斷外面八成在下雨。

若X 是要輸入的隨機(jī)變量，則Y 是要輸出的目標(biāo)類別。對(duì)X 進(jìn)行分類，即使求的使P(Y|X) ***的Y值。若X 為n 維特征變量 X = {A1, A2, …..An} ，若輸出類別集合為Y = {C1, C2, …. Cm} 。

X 所屬最有可能類別 y = argmax P(Y|X), 進(jìn)行如下推導(dǎo)：

樸素貝葉斯的學(xué)習(xí)

有公式可知，欲求分類結(jié)果，須知如下變量：

各個(gè)類別的條件概率，

輸入隨機(jī)變量的特質(zhì)值的條件概率

示例代碼:

import copy 
 
class native_bayes_t: 
     
    def __init__(self, character_vec_, class_vec_): 
        """ 
        構(gòu)造的時(shí)候需要傳入特征向量的值，以數(shù)組方式傳入 
        參數(shù)1 character_vec_ 格式為 [("character_name",["","",""])] 
        參數(shù)2 為包含所有類別的數(shù)組 格式為["class_X", "class_Y"] 
        """ 
        self.class_set = {} 
        # 記錄該類別下各個(gè)特征值的條件概率 
        character_condition_per = {} 
        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,  # 記錄該類別下該特征值在訓(xùn)練樣本中的數(shù)量, 
                    'condition_per' : 0.0 # 記錄該類別下各個(gè)特征值的條件概率 
                } 
        for class_name in class_vec: 
            self.class_set[class_name] = { 
                'num'                     : 0,  # 記錄該類別在訓(xùn)練樣本中的數(shù)量, 
                'class_per'               : 0.0, # 記錄該類別在訓(xùn)練樣本中的先驗(yàn)概率, 
                'character_condition_per' : copy.deepcopy(character_condition_per), 
            } 
 
        #print("init", character_vec_, self.class_set) #for debug 
 
    def learn(self, sample_): 
        """ 
        learn 參數(shù)為訓(xùn)練的樣本，格式為 
        [ 
            { 
                'character'  : {'character_A':'A1'}, #特征向量 
                'class_name' : 'class_X'             #類別名稱 
            } 
        ] 
        """ 
        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 
 
            # 各個(gè)特質(zhì)值數(shù)量加1 
            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['num'] += 1 
 
        # 數(shù)量計(jì)算完畢， 計(jì)算最終的概率值 
        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] 
            # 計(jì)算類別的先驗(yàn)概率 
            data_for_class['class_per'] = float(data_for_class['num']) / sample_num 
 
            # 各個(gè)特質(zhì)值的條件概率 
            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_): 
        """ 
            對(duì)輸入進(jìn)行分類，輸入input的格式為 
        { 
            "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'] 
            # 計(jì)算各個(gè)特征值條件概率的乘積 
            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 
 
character_vec = [("character_A",["A1","A2","A3"]), ("character_B",["B1","B2","B3"])] 
class_vec     = ["class_X", "class_Y"] 
bayes = native_bayes_t(character_vec, class_vec) 
 
 
sample = [ 
            { 
                'character'  : {'character_A':'A1', 'character_B':'B1'}, #特征向量 
                'class_name' : 'class_X'             #類別名稱 
            }, 
            { 
                'character'  : {'character_A':'A3', 'character_B':'B1'}, #特征向量 
                'class_name' : 'class_X'             #類別名稱 
            }, 
            { 
                'character'  : {'character_A':'A3', 'character_B':'B3'}, #特征向量 
                'class_name' : 'class_X'             #類別名稱 
            }, 
            { 
                'character'  : {'character_A':'A2', 'character_B':'B2'}, #特征向量 
                'class_name' : 'class_X'             #類別名稱 
            }, 
            { 
                'character'  : {'character_A':'A2', 'character_B':'B2'}, #特征向量 
                'class_name' : 'class_Y'             #類別名稱 
            }, 
            { 
                'character'  : {'character_A':'A3', 'character_B':'B1'}, #特征向量 
                'class_name' : 'class_Y'             #類別名稱 
            }, 
            { 
                'character'  : {'character_A':'A1', 'character_B':'B3'}, #特征向量 
                'class_name' : 'class_Y'             #類別名稱 
            }, 
            { 
                'character'  : {'character_A':'A1', 'character_B':'B3'}, #特征向量 
                'class_name' : 'class_Y'             #類別名稱 
            }, 
             
        ] 
 
input_data ={ 
    "character_A":"A1", 
    "character_B":"B3", 
} 
 
bayes.learn(sample) 
print(bayes.classify(input_data)) 

總結(jié)：

樸素貝葉斯分類實(shí)現(xiàn)簡單，預(yù)測的效率較高

樸素貝葉斯成立的假設(shè)是個(gè)特征向量各個(gè)屬性條件獨(dú)立，建模的時(shí)候需要特別注意

原文鏈接：http://www.cnblogs.com/zhiranok/archive/2012/09/22/native_bayes.html

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