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Direct Importance Estimation with Model Selection and Its Application to Covariate Shift Adaptation

机译：选择模型的直接重要性估计及其在协变量移位自适应中的应用

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摘要

A situation where training and test samples follow different input distributions is called covariate shift. Under covariate shift, standard learning methods such as maximum likelihood estimation are no longer consistent-weighted variants according to the ratio of test and training input densities are consistent. Therefore, accurately estimating the density ratio, called the importance, is one of the key issues in covariate shift adaptation. A naive approach to this task is to first estimate training and test input densities separately and then estimate the importance by taking the ratio of the estimated densities. However, this naive approach tends to perform poorly since density estimation is a hard task particularly in high dimensional cases. In this paper, we propose a direct importance estimation method that does not involve density estimation. Our method is equipped with a natural cross validation procedure and hence tuning parameters such as the kernel width can be objectively optimized. Simulations illustrate the usefulness of our approach.
机译：训练样本和测试样本遵循不同输入分布的情况称为协变量平移。在协变量平移下，根据测试和训练输入密度的比率一致，诸如最大似然估计之类的标准学习方法不再是一致加权变量。因此，准确估计密度比（重要性）是协变量偏移自适应的关键问题之一。天真的方法是首先分别估计训练和测试输入的密度，然后通过采用估计密度的比率来估计重要性。但是，由于密度估计是一项艰巨的任务，特别是在高维情况下，这种幼稚的方法往往性能较差。在本文中，我们提出了一种不涉及密度估计的直接重要性估计方法。我们的方法配备了自然的交叉验证程序，因此可以客观地优化诸如内核宽度之类的调整参数。仿真说明了我们方法的有效性。

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