[英]What is the marginal probabilities formula used in CRF++?
CRF++ says it can: CRF ++表示可以:
"Can output marginal probabilities for all candidates" on its page: http://crfpp.sourceforge.net/ 其页面上的“可以为所有候选人输出边际概率”: http : //crfpp.sourceforge.net/
But what's the notation of the formula that's used to find these probabilities, in conditional random fields? 但是,在条件随机字段中用于发现这些概率的公式的表示法是什么?
Someone told me it's not simply p(a|b)
, because conditional random fields use context from adjacent observations. 有人告诉我,这不是简单的
p(a|b)
,因为条件随机字段使用了来自相邻观测值的上下文。
What exactly are these marginal probabilities? 这些边际概率到底是什么?
The conditional probability is just p(y|x)
where y
is a sequence of labels and x
is the associated observed sequence. 条件概率就是
p(y|x)
,其中y
是标记序列, x
是相关的观察序列。
The expression for this probability is just the softmax function \\exp( a_i ) / \\sum_{i'} \\exp ( a_{i'})
. 此概率的表达式只是softmax函数
\\exp( a_i ) / \\sum_{i'} \\exp ( a_{i'})
。
For a CRF, a_i
is a function of the label sequence a_i = w \\cdot \\phi(x,y)
, where \\phi(x,y)
is a feature vector derived from a sequence and its labels. 对于CRF,
a_i
是标签序列a_i = w \\cdot \\phi(x,y)
,其中\\phi(x,y)
是从序列及其标签派生的特征向量。
This means that the sum in the denominator is over the exponential number of possible labels, \\mathcal{Y}
: 这意味着分母中的总和超过可能的标签
\\mathcal{Y}
的指数数量:
\sum_{y' \in \mathcal{Y}} \exp ( w \cdot \phi(x,y) )
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