Unit 3 12 General Bayes NetworksYouTube↗  IA↗(long shot)
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[Thrun] So we're now ready to define Bayes networks in a more general way.
我们现在可以用一种更通用的方式定义贝叶斯网络。
Bayes networks define probability distributions over graphs or random variables.
贝叶斯网络定义图表或随机变量的概率分布。
Here is an example graph of 5 variables,
这里是一个5个变量的图的例子，
and this Bayes network defines the distribution over those 5 random variables.
这个贝叶斯网络定义了这5个随机变量的分布。
Instead of enumerating all possibilities of combinations of these 5 random variables,
不同于枚举所有这5个随机变量的可能组合，
the Bayes network is defined by probability distributions
贝叶斯网络的定义产生自
that are inherent to each individual node.
每一个节点的固有的概率分布。
For node A and B, we just have a distribution P of A and P of B
对于节点A和B，我们有A的概率分布，和B的概率分布
because A and B have no incoming arcs.
因为A和B有没有传入箭头。
C is a conditional distribution conditioned on A and B.
C是A和B的条件下的条件分布
D and E are conditioned on C.
D和E​​是在C的条件下。
The joint probability represented by a Bayes network
由一个贝叶斯网络表示的联合概率
is the product of various Bayes network probabilities
是多个对个别节点定义的
that are defined over individual nodes
贝叶斯网络概率的结果。
where each node's probability is only conditioned on the incoming arcs.
每个节点的概率只在传入箭头的条件下。
So A has no incoming arc; therefore, we just want it P of A.
A没有传入箭头，因此，我们只要A的概率。
C has 2 incoming arcs, so we define the probability of C conditioned on A and B.
C有2个传入的箭头，所以我们定义在A和B的条件下C的概率
And D and E have 1 incoming arc that's shown over here.
D和E​​有1个传入箭头，就在这里。
The definition of this joint distribution by using the following factors
这个使用下列因子来定义的联合分布
has one really big advantage.
有一个极大的优势。
Whereas the joint distribution over any 5 variables requires 2 to the 5 minus 1,
任何5个变量的联合分布需要2的5次方减1，
which is 31 probability values,
也就是31个概率值，
the Bayes network over here only requires 10 such values.
而这里的贝叶斯网络只需要10个这样的值。
P of A is one value, for which we can derive P of not A.
A的概率是一个值，由此我们可以得出非A的概率。
Same for P of B.
B是同样的。
P of C given A B is derived by a distribution over C
条件AB下C的概率，来自
conditioned on any combination of A and B, of which there are 4 of A and B as binary.
C在条件A和B的任意组合下的分布，而A和B的有无共有4种情况。
P of D given C is 2 parameters for P of D given C and P of D given not C.
条件C下D的概率有两个参数，分别是条件C下D的概率和条件非C下D的概率
And the same is true for P of E given C.
对条件C下E的概率是同样的。
So if you add those up, you get 10 parameters in total.
所以，如果你将这些加起来，你会得到共10个参数。
So the compactness of the Bayes network
因此，贝叶斯网络的紧凑性
leads to a representation that scales significantly better to large networks
使其在表示大型网络时，
than the common natorial approach which goes through all combinations of variable values.
比通过遍历变量值的所有组合的普通组合做法，要有效得多。
That is a key advantage of Bayes networks,
这是贝叶斯网络的一个关键优势，
and that is the reason why Bayes networks are being used so extensively
这就是为什么贝叶斯网络被如此广泛的用于
for all kinds of problems.
处理各种问题。
So here is a quiz.
因此，这里是道测验题。
How many probability values are required to specify this Bayes network?
表示此贝叶斯网络需要多少个概率值？
Please put your answer in the following box.
请把你的答案填在下面的框中。
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