论文标题
仪器可变回归通过内核最大力矩损失
Instrumental Variable Regression via Kernel Maximum Moment Loss
论文作者
论文摘要
我们研究了基于被称为最大力矩限制（MMR）的核矩限制（CMR）的非线性仪器变量（IV）回归的简单目标。 MMR物镜是通过最大化繁殖核Hilbert Space（RKHS）中属于单位球的残差与仪器之间的相互作用来提出的。首先，它使我们能够将IV回归简化为经验风险最小化问题，其中风险功能取决于仪器上的繁殖核，并且可以通过U统计或V统计量来估算。其次，基于此简化，我们能够在参数和非参数设置中提供一致性和渐近正态性。最后，我们提供易于使用的IV回归算法，并具有有效的超参数选择程序。我们使用在合成和现实世界数据上的实验证明了算法的有效性。
We investigate a simple objective for nonlinear instrumental variable (IV) regression based on a kernelized conditional moment restriction (CMR) known as a maximum moment restriction (MMR). The MMR objective is formulated by maximizing the interaction between the residual and the instruments belonging to a unit ball in a reproducing kernel Hilbert space (RKHS). First, it allows us to simplify the IV regression as an empirical risk minimization problem, where the risk functional depends on the reproducing kernel on the instrument and can be estimated by a U-statistic or V-statistic. Second, based on this simplification, we are able to provide the consistency and asymptotic normality results in both parametric and nonparametric settings. Lastly, we provide easy-to-use IV regression algorithms with an efficient hyper-parameter selection procedure. We demonstrate the effectiveness of our algorithms using experiments on both synthetic and real-world data.
