Conformal predictors are an important class of algorithms that allow
predictions to be made with a user-defined confidence level. They are able to
do this by outputting prediction sets, rather than simple point predictions.
The conformal predictor is valid in the sense that the accuracy of its
predictions is guaranteed to meet the confidence level, only assuming
exchangeability in the data. Since accuracy is guaranteed, the performance of a
conformal predictor is measured through the efficiency of the prediction sets.
Typically, a conformal predictor is built on an underlying machine learning
algorithm and hence its predictive power is inherited from this algorithm.
However, since the underlying machine learning algorithm is not trained with
the objective of minimizing predictive efficiency it means that the resulting
conformal predictor may be sub-optimal and not aligned sufficiently to this
objective. Hence, in this study we consider an approach to train the conformal
predictor directly with maximum predictive efficiency as the optimization
objective, and we focus specifically on the inductive conformal predictor for
classification. To do this, the conformal predictor is approximated by a
differentiable objective function and gradient descent used to optimize it. The
resulting parameter estimates are then passed to a proper inductive conformal
predictor to give valid prediction sets. We test the method on several real
world data sets and find that the method is promising and in most cases gives
improved predictive efficiency against a baseline conformal predictor.

本文研究了使用最大预测效率作为优化目标训练归纳一致预测器（inductive conformal predictor）的方法，将对可用于分类的归纳一致预测器进行了特别关注，并在几个真实数据集上进行了测试，结果表明该方法在大多数情况下相对于基线一致预测器具有更高的预测效率。

使用梯度下降逼近优化的拟合分类

Optimized conformal classification using gradient descent approximation

This paper applies conformal prediction techniques to compute simultaneous
prediction bands and clustering trees for functional data. These tools can be
used to detect outliers and clusters. Both our prediction bands and clustering
trees provide prediction sets for the underlying stochastic process with a
guaranteed finite sample behavior, under no distributional assumptions. The
prediction sets are also informative in that they correspond to the high
density region of the underlying process. While ordinary conformal prediction
has high computational cost for functional data, we use the inductive conformal
predictor, together with several novel choices of conformity scores, to
simplify the computation. Our methods are illustrated on some real data
examples.

本文使用符合预测技术计算功能数据的同时预测带和聚类树。我们使用多个新颖的一致性分数来简化计算，并且在不假设任何分布的情况下，为基础随机过程提供了预测集，并提供信息指向潜在进程的高密度区域。