论文标题
多输出回归的精确和近似保形推断
Exact and Approximate Conformal Inference for Multi-Output Regression
论文作者
论文摘要
给定协变量信息$ x $，机器学习估计$ y $的响应$ y $很常见。但是，仅这些预测并不能量化与上述预测相关的任何不确定性。克服这种缺陷的一种方法是使用保形推理方法，该方法构建了一个包含未观察到的响应$ y $的集合，并具有规定的概率。不幸的是，即使有一维的响应，尽管最近的进步令人鼓舞，但保形推断在计算上还是计算昂贵的。在本文中，我们探讨了多输出回归，当预测模型被描述为$ y $的线性函数时，提供了共形推理$ p $值的精确推导。此外，我们提出\ texttt {unioncp}和\ texttt {rootcp}的多元扩展，作为近似多种多数预测指标的保形预测区域的有效方法，即线性和非线性，同时确保计算优势。我们还提供了使用现实世界和模拟数据的这些方法有效性的理论和经验证据。
It is common in machine learning to estimate a response $y$ given covariate information $x$. However, these predictions alone do not quantify any uncertainty associated with said predictions. One way to overcome this deficiency is with conformal inference methods, which construct a set containing the unobserved response $y$ with a prescribed probability. Unfortunately, even with a one-dimensional response, conformal inference is computationally expensive despite recent encouraging advances. In this paper, we explore multi-output regression, delivering exact derivations of conformal inference $p$-values when the predictive model can be described as a linear function of $y$. Additionally, we propose \texttt{unionCP} and a multivariate extension of \texttt{rootCP} as efficient ways of approximating the conformal prediction region for a wide array of multi-output predictors, both linear and nonlinear, while preserving computational advantages. We also provide both theoretical and empirical evidence of the effectiveness of these methods using both real-world and simulated data.
