We consider the problem of distribution-free predictive inference, with the
goal of producing predictive coverage guarantees that hold conditionally rather
than marginally. Existing methods such as conformal prediction offer marginal
coverage guarantees, where predictive coverage holds on average over all
possible test points, but this is not sufficient for many practical
applications where we would like to know that our predictions are valid for a
given individual, not merely on average over a population. On the other hand,
exact conditional inference guarantees are known to be impossible without
imposing assumptions on the underlying distribution. In this work we aim to
explore the space in between these two, and examine what types of relaxations
of the conditional coverage property would alleviate some of the practical
concerns with marginal coverage guarantees while still being possible to
achieve in a distribution-free setting.

本文考虑面向分布无关的预测推断问题，目标是生成有条件而非边缘的预测覆盖保证。我们旨在探索边缘覆盖保证的实际问题，并研究一些能够缓解一些实际关注的条件覆盖性质松弛类型，同时仍能在分布无关的环境下实现。

无分布条件预测推断的局限性

The limits of distribution-free conditional predictive inference

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 {\it
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, in order
to adapt to heteroskedascity in the data. Finally, we propose a model-free
notion of variable importance, called {\it leave-one-covariate-out} or LOCO
inference. Accompanying this paper is an R package {\tt 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.

本文提出了基于顺应性推断的无分布预测推断的一般框架，并通过分析和比较其两个主要变体：完整顺应性推断和分裂顺应性推断以及相关的 jackknife 法，作出了在统计准确度和计算效率之间的不同权衡。与此同时，本文还发展了一种构建有效样本内预测间隔的方法，称为 “排名为一” 的顺应性推断。本文提出的所有提案的实施都可以使用 R 包 “conformalInference” 进行。