We develop fast distribution-free conformal prediction algorithms for obtaining multivalid coverage on exchangeable data in the batch setting. Multivalid coverage guarantees are stronger than marginal coverage guarantees in two ways: (1) They hold even conditional on group membership -- that is, the target coverage level $1-\alpha$ holds conditionally on membership in each of an arbitrary (potentially intersecting) group in a finite collection $\mathcal{G}$ of regions in the feature space. (2) They hold even conditional on the value of the threshold used to produce the prediction set on a given example. In fact multivalid coverage guarantees hold even when conditioning on group membership and threshold value simultaneously. We give two algorithms: both take as input an arbitrary non-conformity score and an arbitrary collection of possibly intersecting groups $\mathcal{G}$, and then can equip arbitrary black-box predictors with prediction sets. Our first algorithm (BatchGCP) is a direct extension of quantile regression, needs to solve only a single convex minimization problem, and produces an estimator which has group-conditional guarantees for each group in $\mathcal{G}$. Our second algorithm (BatchMVP) is iterative, and gives the full guarantees of multivalid conformal prediction: prediction sets that are valid conditionally both on group membership and non-conformity threshold. We evaluate the performance of both of our algorithms in an extensive set of experiments. Code to replicate all of our experiments can be found at https://github.com/ProgBelarus/BatchMultivalidConformal
翻译:在批量设置中,我们为获得可交换数据的多价覆盖开发了快速且不流通的符合预测算法。多价覆盖保证比边际覆盖保证更强,有两种方式:(1) 它们甚至以群体成员资格为条件,即目标覆盖水平为1美元-阿尔法$以每个任意(潜在交叉)组的成员资格为条件,在一定的集合中,在特性空间中,每个(潜在交叉)组的会员资格为条件。(2) 它们甚至以用于生成可交换数据的可交换数据的临界值为条件。事实上,多价覆盖保证即使同时调节群体成员资格和阈值也维持在边缘范围。我们给出两种算法:(1) 它们都以任意的不合规分数为条件,可能任意收集一个任意的(可能交叉的)组的会员资格为条件。 我们的第一种算法(BatchGCP)直接扩展了微缩缩缩缩图,只需要解决一个单一的折叠式最小化问题,并产生一个具有组合-定值保证的第二位数。我们每个组的不固定的运算算法,在美元/Calalalalslationalalalalslationslationslationslationslevalslationsalslevalslevalslationslevationslevalslevalsleval) lax, 和我们每个组的组合都做出一个完整的预测。