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arXiv 2302.02552cs.LGstat.ML
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通过在线密度比估计适应连续协变量偏移

Adapting to Continuous Covariate Shift via Online Density Ratio Estimation

The University of Tokyo(东京大学);RIKEN AIP(理化学研究所人工智能项目);Nanjing University(南京大学)

Yu-Jie Zhang, Zhen-Yu Zhang, Peng Zhao, Masashi Sugiyama

AI总结:

本文针对连续协变量偏移场景,提出在线密度比估计方法以重用历史信息,实现预测器累积风险最小化,并给出动态遗憾界与超额风险保证。

摘要:

处理分布偏移是现代机器学习面临的核心挑战之一。一个基本情形是协变量偏移,即数据输入分布从训练阶段到测试阶段发生变化,而输入条件下的输出分布保持不变。本文开创性地研究了一个更具挑战性的场景——连续协变量偏移,其中测试数据按顺序出现,且其分布可能连续变化。我们的目标是自适应地训练预测器,使其随时间累积的预测风险最小化。从重要性加权学习出发,我们证明了如果测试输入与训练输入的时变密度比能够被准确估计,该方法便能有效工作。然而,现有的密度比估计方法会因每个时间步的数据稀缺而失效。为此,我们提出了一种能够适当重用历史信息的在线方法。我们证明了所提出的密度比估计方法具有动态遗憾界,从而表现良好,并最终为预测器提供了超额风险保证。实验结果也验证了其有效性。

英文摘要:

Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from training to testing stages while the input-conditional output distribution remains unchanged. In this paper, we initiate the study of a more challenging scenario -- continuous covariate shift -- in which the test data appear sequentially, and their distributions can shift continuously. Our goal is to adaptively train the predictor such that its prediction risk accumulated over time can be minimized. Starting with the importance-weighted learning, we show the method works effectively if the time-varying density ratios of test and train inputs can be accurately estimated. However, existing density ratio estimation methods would fail due to data scarcity at each time step. To this end, we propose an online method that can appropriately reuse historical information. Our density ratio estimation method is proven to perform well by enjoying a dynamic regret bound, which finally leads to an excess risk guarantee for the predictor. Empirical results also validate the effectiveness.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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