作为随机变量的效用：密度估计和结构发现
Utilities as Random Variables: Density Estimation and Structure Discovery
摘要：
决策理论传统上不包括效用函数的不确定性。我们认为，一个人的效用值为一个给定的结果可以被视为我们对待其他领域的属性：作为一个随机变量的密度函数在其可能的值。我们表明，我们可以应用统计密度估计技术来学习这样的密度函数从数据库中的部分引出的效用函数。特别是，我们为这个问题定义了一个贝叶斯学习框架，假设效用分布是高斯分布的混合，其中混合成分代表统计上一致的子群体。我们还可以将我们的技术扩展到发现人口中的效用函数的广义可加性结构的问题。我们定义了效用函数结构的贝叶斯模型选择准则和结构上的搜索过程。学习模型中效用的因式分解，以及从密度估计中获得的泛化，使我们能够使用数量少得多的效用启发问题来提供对效用的鲁棒估计。我们的实验与我们的技术合成效用数据和实用功能在产前诊断领域的一个真正的数据库。
英文摘要：
Decision theory does not traditionally include uncertainty over utility functions. We argue that the a person's utility value for a given outcome can be treated as we treat other domain attributes: as a random variable with a density function over its possible values. We show that we can apply statistical density estimation techniques to learn such a density function from a database of partially elicited utility functions. In particular, we define a Bayesian learning framework for this problem, assuming the distribution over utilities is a mixture of Gaussians, where the mixture components represent statistically coherent subpopulations. We can also extend our techniques to the problem of discovering generalized additivity structure in the utility functions in the population. We define a Bayesian model selection criterion for utility function structure and a search procedure over structures. The factorization of the utilities in the learned model, and the generalization obtained from density estimation, allows us to provide robust estimates of utilities using a significantly smaller number of utility elicitation questions. We experiment with our technique on synthetic utility data and on a real database of utility functions in the domain of prenatal diagnosis.
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