论文标题
独立测试没有地面真理的嘈杂学习者
Independence Tests Without Ground Truth for Noisy Learners
论文作者
论文摘要
可以为任意相关的二进制分类器编写确切的地面真实不变的多项式系统。他们的解决方案给出了样本统计数据的估计，这些样本统计需要了解样品中正确标签的基础真理。在这些多项式系统中，只有少数以封闭形式解决。在这里，我们讨论了独立二进制分类器的确切解决方案 - 解决了本次会议上提出的杰出问题。它的实际适用性受到其唯一剩余假设的阻碍 - 分类器需要在其样本错误中独立。我们讨论如何使用封闭形式解决方案创建一个自洽测试，该测试可以验证独立性假设本身而没有正确的标签真实。它可以作为尚未解决的二进制分类器的代数几何猜想。对于标量回归器的地面真实代数系统的类似猜想是可以解决的，我们在此处介绍了解决方案。我们还讨论了Penn ML基准分类任务的实验，这些实验提供了进一步的证据，表明该猜想对于二元分类器的多项式系统可能是正确的。
Exact ground truth invariant polynomial systems can be written for arbitrarily correlated binary classifiers. Their solutions give estimates for sample statistics that require knowledge of the ground truth of the correct labels in the sample. Of these polynomial systems, only a few have been solved in closed form. Here we discuss the exact solution for independent binary classifiers - resolving an outstanding problem that has been presented at this conference and others. Its practical applicability is hampered by its sole remaining assumption - the classifiers need to be independent in their sample errors. We discuss how to use the closed form solution to create a self-consistent test that can validate the independence assumption itself absent the correct labels ground truth. It can be cast as an algebraic geometry conjecture for binary classifiers that remains unsolved. A similar conjecture for the ground truth invariant algebraic system for scalar regressors is solvable, and we present the solution here. We also discuss experiments on the Penn ML Benchmark classification tasks that provide further evidence that the conjecture may be true for the polynomial system of binary classifiers.
