Quantifying Confidence for Computer-Intensive Classifiers

分类是关于从协变量的向量X中预测具有许多潜在值的类标签Y。传统上，这相当于选择一个分类器或基于一组训练观察值来估计给定X = x的Y的条件分布。为了量化每个实例的置信度（即具有未知类成员Y的未来观测X），还可以使用某些p值来提供一组合理的类标签。后一种方法的一个优点是不需要关于不同类别概率的先验信息，并且存在基于排列检验的非参数过程，其在最小假设下是有效的。在本项目中，后一种方法在各个方向上扩展，特别是：（i）底层分类器应该适度稳健，这需要计算上可行的程序。多元M-估计的最新进展将有助于这方面的工作。(ii)考虑到支持向量机和其他大间隔分类器的成功与复杂性惩罚的结合，需要开发相应的p值。一个主要的概念性问题是数据驱动的调优参数选择。(iii)我们希望发展一般理论的渐近性质，这些方法时，样本量和尺寸的X都在增长。

Classification is about prediction a class label Y with finitely many potential values from a vector X of covariables. Traditionally this amounts to choosing a classifier or estimating the conditional distributions of Y given X = x based on a set of training observations. To quantify the confidence for each instance (i.e. future observation X with unknown class membership Y ), one can also use certain p-values to provide a set of plausible class labels. One advantage of the latter approach is that prior information about the different classes’ probability isn’t needed, and there are nonparametric procedures based on permutation tests which are valid under minimal assumptions. In the present project, the latter methods are extended in various directions, in particular: (i) The underlying classifiers should be moderately robust which necessitates computationally feasible procedures. Recent progress in multivariate M-estimation will be helpful in this respect. (ii) Given the success of support vector machines and other large margin classifiers in combination with complexity penalties, it is desirable to develop corresponding p-values. A major conceptual problem will be the data-driven choice of tuning parameters. (iii) We want to develop general theory for the asymptotic properties of these methods when both the sample size and the dimension of X are growing.