Distribution-Free Predictive Inference for Regression
Distribution-Free Predictive Inference for Regression
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DOI：
10.1080/01621459.2017.1307116
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发表时间：
2018-01-01
影响因子：
3.7
通讯作者：
Wasserman, Larry
中科院分区：
文献类型：
--
作者：
Lei, Jing;G'Sell, Max;Wasserman, Larry
我们开发了一个通用的框架，用于回归中的无分布预测推理，使用共形推理。所提出的方法允许使用回归函数的任何估计器来构建响应变量的预测带。由此得到的预测带保留了标准假设下原始估计器的一致性属性，同时保证了有限样本的边际覆盖，即使这些假设不成立。我们从经验和理论上分析和比较了我们的共形框架的两个主要变体：完全共形推理和分裂共形推理，以及相关的折刀方法。这些方法在统计精度(结果预测间隔的长度)和计算效率之间提供了不同的折衷。作为扩展，我们发展了一种构造有效样本内预测区间的方法，称为秩1-OUT共形推理，该方法具有与分裂共形推理相同的计算效率。我们还描述了我们的程序的扩展，以产生局部可变的长度的预测带，以适应数据中的异方差。最后，我们提出了一种无模型的变量重要性概念，称为留单协变量剔除或局部推理。本文附带了一个R包conformalInference，它实现了我们介绍的所有建议。本着可再现性的精神，我们所有的经验结果也可以使用这个包轻松(重新)生成。
We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We analyze and compare, both empirically and theoretically, the two major variants of our conformal framework: full conformal inference and split conformal inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. As extensions, we develop a method for constructing valid in-sample prediction intervals called rank-one-out conformal inference, which has essentially the same computational efficiency as split conformal inference. We also describe an extension of our procedures for producing prediction bands with locally varying length, to adapt to heteroscedasticity in the data. Finally, we propose a model-free notion of variable importance, called leave-one-covariate-out or LOCO inference. Accompanying this article is an R package conformalInference that implements all of the proposals we have introduced. In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package.