Existing frameworks for probabilistic inference assume the inferential target is the posited statistical model's parameter. In machine learning applications, however, often there is no statistical model, so the quantity of interest is not a model parameter but a statistical functional. In this paper, we develop a generalized inferential model framework for cases when this functional is a risk minimizer or solution to an estimating equation. We construct a data-dependent possibility measure for uncertainty quantification and inference whose computation is based on the bootstrap. We then prove that this new generalized inferential model provides approximately valid inference in the sense that the plausibility values assigned to hypotheses about the unknowns are asymptotically well-calibrated in a frequentist sense. Among other things, this implies that confidence regions for the underlying functional derived from our new generalized inferential model are approximately valid. The method is shown to perform well in classical examples, including quantile regression, and in a personalized medicine application.

翻译：概率推论的现有假设框架假定了假设的统计模型参数。 然而,在机器学习应用中,往往没有统计模型,因此利息的数量不是一个模型参数,而是一个统计功能。在本文中,我们为这种功能是风险最小化或估算方程解决办法的情况制定了普遍推论模型框架。我们为根据靴子陷阱计算出的不确定性量化和推论构建了一个数据依赖的可能性计量尺度。然后,我们证明这一新的普遍推论模型提供了大致有效的推论,因为赋予未知物假设的概率值在常态意义上是一样的,因此,在常态意义上是相当相近的。这意味着,对于我们新的通用推论模型产生的基本功能的信任区域大致有效。这种方法在古典例子中表现良好,包括四分回归,在个化医学应用中表现良好。