Conditional validity and length efficiency are two crucial aspects of
conformal prediction (CP). Achieving conditional validity ensures accurate
uncertainty quantification for data subpopulations, while proper length
efficiency ensures that the prediction sets remain informative and non-trivial.
Despite significant efforts to address each of these issues individually, a
principled framework that reconciles these two objectives has been missing in
the CP literature. In this paper, we develop Conformal Prediction with
Length-Optimization (CPL) - a novel framework that constructs prediction sets
with (near-) optimal length while ensuring conditional validity under various
classes of covariate shifts, including the key cases of marginal and
group-conditional coverage. In the infinite sample regime, we provide strong
duality results which indicate that CPL achieves conditional validity and
length optimality. In the finite sample regime, we show that CPL constructs
conditionally valid prediction sets. Our extensive empirical evaluations
demonstrate the superior prediction set size performance of CPL compared to
state-of-the-art methods across diverse real-world and synthetic datasets in
classification, regression, and text-related settings.

研究发展了一种新颖的基于长度优化的一致性预测框架（CPL），能够在不同类别的协变量转移下确保条件有效性，并构建出（接近）最优长度的预测集合，通过广泛的实证评估验证了其在分类、回归和文本相关设置方面相较于最新方法在预测集大小性能方面的优越性。

置信度预测中的长度优化

Length Optimization in Conformal Prediction

Conformal Prediction (CP) algorithms estimate the uncertainty of a prediction
model by calibrating its outputs on labeled data. The same calibration scheme
usually applies to any model and data without modifications. The obtained
prediction intervals are valid by construction but could be inefficient, i.e.
unnecessarily big, if the prediction errors are not uniformly distributed over
the input space.
We present a general scheme to localize the intervals by training the
calibration process. The standard prediction error is replaced by an optimized
distance metric that depends explicitly on the object attributes. Learning the
optimal metric is equivalent to training a Normalizing Flow that acts on the
joint distribution of the errors and the inputs. Unlike the Error Re-weighting
CP algorithm of Papadopoulos et al. (2008), the framework allows estimating the
gap between nominal and empirical conditional validity. The approach is
compatible with existing locally-adaptive CP strategies based on re-weighting
the calibration samples and applies to any point-prediction model without
retraining.

用标定的数据校准预测模型的不确定性，通过训练标定过程以实现区间的本地化，选择适当的距离度量代替标准预测误差，并通过训练来学习最优度量，从而充分应用于现有的局部适应性标定策略，适用于任何点预测模型。

用于一致回归的正规流

Normalizing Flows for Conformal Regression

Conformal predictors are set predictors that are automatically valid in the
sense of having coverage probability equal to or exceeding a given confidence
level. Inductive conformal predictors are a computationally efficient version
of conformal predictors satisfying the same property of validity. However,
inductive conformal predictors have been only known to control unconditional
coverage probability. This paper explores various versions of conditional
validity and various ways to achieve them using inductive conformal predictors
and their modifications.

本文探讨了使用归纳一致性预测器及其修改版本实现有条件有效性的各种方法，以及这些方法在覆盖率概率和计算效率方面的表现。