论文标题
可靠和可扩展的非参数多类概率估计的线性算法
Linear Algorithms for Robust and Scalable Nonparametric Multiclass Probability Estimation
论文作者
论文摘要
多类概率估计是估计属于类协变量信息的数据点的条件概率的问题。它在统计分析和数据科学中有广泛的应用。最近，已经开发了一类加权支持矢量机（WSVM），以通过$ k $ - 类问题的集合学习来估计类概率（Wu，Zhang and Liu，2010； Wang，Zhang和Wu，2019年），其中$ k $是班级的数量。估计器非常强大，可以实现概率估计的高精度，但是它们的学习是通过成对耦合实施的，这需要$ k $中的多项式时间。在本文中，我们提出了两种新的学习方案，即基线学习和One-All（OVA）学习，以进一步提高计算效率和估计准确性的WSVM。特别是，基线学习具有最佳的计算复杂性，因为它在$ k $中是线性的。尽管不是最有效的计算效率，但OVA在比较的所有程序中提供了最佳的估计准确性。最终的估计器是无分布的，并且显示为一致。我们进一步进行广泛的数值实验以证明有限的样本性能。
Multiclass probability estimation is the problem of estimating conditional probabilities of a data point belonging to a class given its covariate information. It has broad applications in statistical analysis and data science. Recently a class of weighted Support Vector Machines (wSVMs) has been developed to estimate class probabilities through ensemble learning for $K$-class problems (Wu, Zhang and Liu, 2010; Wang, Zhang and Wu, 2019), where $K$ is the number of classes. The estimators are robust and achieve high accuracy for probability estimation, but their learning is implemented through pairwise coupling, which demands polynomial time in $K$. In this paper, we propose two new learning schemes, the baseline learning and the One-vs-All (OVA) learning, to further improve wSVMs in terms of computational efficiency and estimation accuracy. In particular, the baseline learning has optimal computational complexity in the sense that it is linear in $K$. Though not being most efficient in computation, the OVA offers the best estimation accuracy among all the procedures under comparison. The resulting estimators are distribution-free and shown to be consistent. We further conduct extensive numerical experiments to demonstrate finite sample performance.
