Stated formally, a decision problem may consist of four basic elements: 1) an observation 0 from a random variable 0 , 2) a set of possible decisions (or actions) a e A , 3) the state of nature 669 , and 4) a loss function L(ai,6) which specifies the cost associated with a chosen decision a, given that 6 is the true state of nature.

itself; (2) PfDlSjS is the sentence generative probability that captures the degree of relevance of S j to the residual document D ; and (3) L(Si,Sj) is the loss function that characterizes the relationship between sentence Si and any other sentence S j.

In addition, the introduction of various loss functions also provides the summarization framework with a flexible but systematic way to render the redundancy and coherence relationships among sentences and between sentences and the whole document, respectively.

There are many ways to construct the above mentioned three componen mod ls, i.e., the sentence generative model FED | 513 , the sentence prior model P(Sj), and the loss function L(S,.,Sj).

4.3 Loss function

The loss function introduced in the proposed summarization framework is to measure the relationship between any pair of sentences.

L is a loss function that measures the quality of the classifier, A is a nonnegative regularization parameter that penalizes model complexity, and ||w||2 = wTw.

Different choices for L entail different classifier types; e.g., when choosing the hinge loss function for L one obtains the popular Support Vector Machine classifier (Zhang, 2004).

In particular, the learning rate schedule from PEGASOS is adopted (Shalev-Shwartz et al., 2007), and the modified Huber loss, introduced by Zhang (2004), is chosen as loss function L.3