贝叶斯定理是就是在给定的数据概率来表示未知的后验概率。比如已知某水果是红色的情况下,判断该水果有多大的概率是苹果,用数学符号表示就是
![clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/be4d1a87-c6bc-4a8d-81be-c1f8f3203fa2.gif)
下面的三个概率都是可以通过样本统计简单计算得到的:“一个水果的颜色是红色”的概率P(X);“一个水果是苹果” 的概率 P(H)(先验概率);“如果一个水果是苹果那么它的颜色是红色”的概率
![clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/d7ecbc8d-9da1-46b8-987a-a3a3e9bbaebb.gif)
我们可以推理得到:
![clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/a1a8f331-19de-4298-9622-707e6ec1de53.gif)
![clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/50c458f9-a24e-426f-af5e-32939473c3bc.gif)
=
![clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/ef2f9321-e4b0-4d40-a0ce-081acc64f2f2.gif)
![clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/f13c9da8-9c9e-4963-b059-5ac7fcaae164.gif)
=
![clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/540727f9-4c3e-4d3f-ba15-289e2468cb2d.gif)
=
![clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/ab803502-b13b-4233-a3e0-2aa94887c80e.gif)
抽象得到的公式
![clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/f8054db4-55c6-4501-af32-0a226a48c12f.gif)
贝叶斯分类的基本思路就是把
![clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/6d14719e-a049-4658-b93e-aa8ea5b66584.gif)
![clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/7f1abb1d-8956-490e-8301-5cf6a654139b.gif)
![clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/643a707a-adfd-49a0-af62-ff76d91ef57c.gif)
![clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/fffccccb-a736-467a-9d6d-04a7ee7d40a8.gif)
朴素贝叶斯分类
实际情况要比上面的那个例子复杂一些,因为一个事物的属性是多维的,一个水果的属性可能就要包括:颜色、形状、重量、体积……。
实际上的分类可能是要算这样一个概率:
![clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/98de89f8-d082-4c9b-9505-8b1716001a81.gif)
如果属性相互独立,那么
![clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/706efd46-1b1d-42e1-92fc-721715a9f797.gif)
朴素贝叶斯的朴素之处在于不管属性独不独立,都按独立来算,这样可以使运算大大简化。
归纳一下朴素贝叶斯的运算流程:
1. 每个数据样本用一个n维特征向量
![clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/38a1eecc-b1d5-4821-b006-d40cbf985bf8.gif)
![clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/704a1b53-04d7-4f0a-a68f-f0e1e2474f71.gif)
2. 假定有m个类
![clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/6d6fe90b-763a-4c36-81e5-db6fe793f235.gif)
![clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/b5739927-0b38-45f2-83c1-7846a4a51487.gif)
这样,我们最大化
![clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/db6ea4a2-3810-4b02-ac2a-c3fa8016a94d.gif)
![clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/be43bbb3-68d2-4218-89a8-ffa26a407ff5.gif)
![clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/6d449de4-450b-4dd9-b2b5-1d73e86aef94.gif)
3.由于P(X) 对于所有类为常数,只需要
![clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/c23bc4a2-4d99-4922-a85f-8347270eb1e9.gif)
![clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/fc02d43d-8292-46d6-8ef0-d2b54c58cd76.gif)
![clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/c3e611a5-a00c-44e9-b040-76f1b91e7ffd.gif)
![clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/1ac31792-0ac7-4b8b-8491-32c3113f5101.gif)
![clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/e0ef1c32-cf03-4d70-9c5c-29c1f52b4ec7.gif)
4.给定具有许多属性的数据集,计算
![clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/aa6e6bec-5b6f-4b31-8ccf-33a822e1344a.gif)
![clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/60f15e1f-810d-439b-9470-bb287d19e249.gif)
![clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/b3251ce7-c13a-48d2-aa0f-bbd715b9ef3b.gif)
概率
![clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/7917a618-5a21-4c11-8257-de520029e984.gif)
![clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/e48bd076-abaa-4b44-915e-138ba7c19e69.gif)
![clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/ca056152-4c5a-4df1-9759-bc754c24da11.gif)
(a) 如果Ak是分类属性,则
![clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/121fa2e1-1e92-4608-bb40-ef57ed2b8016.gif)
(b) 如果是连续值属性,则通常假定该属性服从高斯分布。因而,
![clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/6adbdfe4-3706-46f5-b48d-9bacddc2f75e.gif)
其中,给定类Ci的训练样本属性Ak的值,
![clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/488e97a3-1a53-45b1-a6d1-179412e28fdd.gif)
![clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/3a2563a0-a663-4888-85b8-22d01ec979ab.gif)
5.为对未知样本X分类,对每个类Ci,计算
![clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/c845310e-8c0a-40b4-b48f-a2f844af23bf.gif)
![clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/fb7bb41f-d185-4003-90d6-41f5825222d4.gif)
换言之,X被指派到其
![clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/e47885c3-13f6-40d2-8c2c-632339519176.gif)
贝叶斯信念网络
朴素贝叶斯假定属性之间是独立的。贝叶斯信念网络说明联合概率分布,它提供一种因果关系的图形,可以在其上进行学习。
信念网络由两部分定义。第一部分是有向无环图,其每个结点代表一个随机变量,而每条弧代表一个概率依赖。如果一条弧由结点Y到Z,则Y是Z的双亲或直接前驱,而Z是Y的后继。第二部分是每个属性一个条件概率表(CPT)。
下面是一个LungCancer的CPT。
![clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/f2eb56a8-9548-4d0c-bc1d-9d9481360bb8.gif)
在贝叶斯信念网络中对应于属性或变量
![clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/ffdd9c9c-a6db-4901-8f59-ebf104821164.gif)
![clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/853bdefc-7afd-4644-a99b-6b98a3c98780.gif)
![clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/369409f9-aaec-4e55-95eb-5570eca6bfc9.gif)
如上图,对于FamilyHistory,Smoker,LungCancer这三个属性,用朴素贝叶斯计算,得到的联合概率是
![clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/638b6325-7671-45f8-b3f7-49de7a0a978c.gif)
但是如果用贝叶斯信念网络计算得到的联合概率将会是:
![clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/6134dc7f-8535-4d59-99ee-2fb8bd739ab7.gif)
贝叶斯信念网络的问题
1、如果贝叶斯信念网络的网络结构和所有数值都是给定的,那么可以直接进行计算。但是,数据是隐藏的,比如上图中的FamilyHistory/Somker到LungCancer的条件概率是未知的,只是知道存在这样的依存关系,这时就需要进行条件概率的估算。梯度训练算法和EM算法常被用于处理此问题。
2、贝叶斯网络的数据结构可能是未知的,这时就需要根据已知数据启发式学习贝叶斯网络结构。K2算法可用于解决此问题。
梯度训练算法
梯度训练是用于解决信念网络中隐藏数据问题的,就是已知上图(a),但是不知道上图(b)。
设D是d个训练样本
![clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/3d6f4d12-1b07-4465-9cd5-8a1fff246ab1.gif)
![clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/b10f63a7-08ba-4b4c-8ce1-594a049baa76.gif)
![clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/7d8ce6c7-0235-4e37-9441-9e315f563d0a.gif)
![clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/5955a56b-772b-4dd6-b4f9-267057e4be2d.gif)
![clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/b351f143-ce18-4145-b3eb-538f4f1ae46f.gif)
![clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/8d8b114e-c18d-4a42-acf6-dbbbfc8038cc.gif)
![clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/ba78aca4-56ce-4883-baf1-408ddefe66f4.gif)
![clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/8a18c9b5-d988-4196-8f25-ce3abe0e8c81.gif)
![clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/554849ee-0dec-4de7-aaf8-ed4015e5ed32.gif)
![clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/997d2497-52c9-4935-8147-17e4c18a424a.gif)
![clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/a7c058c8-bb38-48f7-8125-29b63f7e4c80.gif)
![clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/5c855a79-5cc8-4df5-a064-e5f86ac0db07.gif)
![clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/1e2c5b21-97d4-4fb2-9f6f-d3a7ef990a90.gif)
![clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/285ad158-0dba-4fc1-a21a-bc43d42180f0.gif)
梯度训练算法就是求出最为满足
![clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/edcfaca1-a084-444b-a3f4-f4aa4da988b7.gif)
![clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/1356a5c7-2ea7-499c-8cab-25acdc797533.gif)
![clip_image100clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/6d36163a-9936-48f2-8efe-7edbc9a647bd.gif)
![clip_image102clip_image100clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/bde7c80f-67b9-497c-9a43-584257645a87.gif)
![clip_image104clip_image102clip_image100clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/893b2193-88d9-43c1-adf4-65501afb40c6.gif)
具体的算法:
1、就是对每一个
![clip_image087[3]clip_image104clip_image102clip_image100clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/4254aa5b-eb41-400d-a9c8-23478c505ff7.gif)
![clip_image107clip_image087[3]clip_image104clip_image102clip_image100clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/faae6cc9-f89e-45d7-ad87-c8e6d5a2bbde.gif)
2、更新权值:沿梯度方向前进一小步。
![clip_image109clip_image107clip_image087[3]clip_image104clip_image102clip_image100clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/a2332d33-7170-4ac5-b7db-40cb4645918e.gif)
3、由于权值
![clip_image087[4]clip_image109clip_image107clip_image087[3]clip_image104clip_image102clip_image100clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/fa197457-727a-4668-9b6e-9afe81117d14.gif)
![clip_image112clip_image087[4]clip_image109clip_image107clip_image087[3]clip_image104clip_image102clip_image100clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/fdd303d2-15e3-4ca4-a175-383d384574fe.gif)
![clip_image114clip_image112clip_image087[4]clip_image109clip_image107clip_image087[3]clip_image104clip_image102clip_image100clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/4d324e75-34e5-460b-b1aa-d6c2f2d2a9c7.gif)
关于
![clip_image087[5]clip_image114clip_image112clip_image087[4]clip_image109clip_image107clip_image087[3]clip_image104clip_image102clip_image100clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/069e68ae-4a76-437b-9a35-7ae49979895b.gif)
![clip_image116clip_image087[5]clip_image114clip_image112clip_image087[4]clip_image109clip_image107clip_image087[3]clip_image104clip_image102clip_image100clip_image097[1]clip_image085[1]clip_image097clip_image087[2]clip_image091[1]clip_image093[2]clip_image089[1]clip_image095[1]clip_image093[1]clip_image087[1]clip_image095clip_image093clip_image091clip_image089clip_image087clip_image085clip_image083clip_image081clip_image079clip_image077clip_image075clip_image073clip_image043[3]clip_image071clip_image043[2]clip_image068clip_image066clip_image064clip_image062clip_image060clip_image058clip_image056clip_image054clip_image051[1]clip_image051clip_image049clip_image043[1]clip_image038[2]clip_image045clip_image043clip_image041clip_image038[1]clip_image038clip_image036clip_image034clip_image032clip_image030clip_image028clip_image026clip_image024clip_image022clip_image020clip_image018clip_image016clip_image014clip_image012clip_image010clip_image008clip_image006clip_image002[1]clip_image004clip_image002朴素贝叶斯与贝叶斯信念网络贝叶斯信念网络](/Files/20116/a0bfbfc9-0bae-43d5-9896-fd0ab5111e15.gif)
最新评论