將一下三塊內(nèi)容結(jié)合起來看比較好：

條件隨機(jī)場的精彩總結(jié)性論述，更多詳細(xì)信息可以參閱連接文章：http://homepages.inf.ed.ac.uk/csutton/publications/crftut-fnt.pdf?
????Much work in learning with graphical models, especially in statistical natural-language processing, has focused on generative models that explicitly attempt to model a joint probability distribution p(y,x) over inputs and outputs. Although this approach has advantages, it also has important limitations. Not only can the dimensionality of x be very large, but the features may have complex dependencies, so constructing a probability distribution over them is difficult. Modeling the dependencies among inputs can lead to intractable models, but ignoring them can lead to reduced performance.

????A solution to this problem is a discriminative approach, similar to that taken in classifiers such as logistic regression. Here we model the conditional distribution p(y|x) directly, which is all that is needed for classification. This is the approach taken by conditional random fields (CRFs). CRFs are essentially a way of combining the advantages of discriminative classification and graphical modeling, combining the ability to compactly model multivariate outputs y with the ability to leverage a large number of input features x for prediction. The advantage to a conditional model is that dependencies that involve only variables in x play no role in the conditional model, so that an accurate conditional

李航-統(tǒng)計(jì)學(xué)習(xí)-線性鏈條件隨機(jī)場
李航的書中對線性鏈條件隨機(jī)場定義為如下所示，一開始難以理解，后來終于搞懂，式子中，索引i代表輸出序列的位置索引，k代表兩個輸出序列之間的轉(zhuǎn)移特征索引，即這種轉(zhuǎn)移可能有多個特征，l代表每個輸出序列位置對應(yīng)的特征索引，即序列中每個節(jié)點(diǎn)也可能有多個特征。t和s只取1或0表征的是此特征是否存在，前面的lamda和mu表征的是每個特征的權(quán)重，這就和下面的神經(jīng)網(wǎng)絡(luò)聯(lián)系在了一起。k個特征表征的是輸出維度，每個維度的標(biāo)量數(shù)值通過此處的權(quán)重來表征。

youtue --?https://www.youtube.com/watch?v=PGBlyKtfB74&list=PL6Xpj9I5qXYEcOhn7TqghAJ6NAPrNmUBH&index=19
下圖為上面視頻中的截圖，利用神經(jīng)網(wǎng)絡(luò)來獲取節(jié)點(diǎn)特征向量，利用矩陣V表征狀態(tài)間的轉(zhuǎn)移特征，李航的書中也有類似的矩陣表示，但是書中的矩陣與此處的矩陣有所不同，具體可以參考原書。

最后CRF是判別模型，概率計(jì)算采用前向后向算法，訓(xùn)練采用極大似然估計(jì)訓(xùn)練，預(yù)測采用維特比算法。目前對書中算法的細(xì)節(jié)沒有仔細(xì)研讀，等有時間再細(xì)看。