Teacher:In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Teacher: Now, understand the problem? Solve this instance: Probabilistic independence can dramatically sim plify the task of eliciting, representing, and com puting with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing no tions of independence for utility functions in a multi-attribute space, and suggest that these can be used to achieve similar advantages. Our new results concern conditional additive in dependence, which we show always has a per fect representation as separation in an undirected graph (a Markov network). Conditional addi tive independencies entail a particular functional form for the utility function that is analogous to a product decomposition of a probability function, and confers analogous benefits. This functional form has been utilized in the Bayesian network and influence diagram literature, but generally without an explanation in terms of independence. The functional form yields a decomposition of the utility function that can greatly speed up expected utility calculations, particularly when the utility graph has a similar topology to the probabilistic network being used.
Student:
Graphical models for preference and utility