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arXiv 2209.07787stat.MLcs.LG
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面向有偏正样本-无标签数据的双重逻辑回归方法

Double logistic regression approach to biased positive-unlabeled data

University of Life Sciences, Warsaw(华沙生命科学大学);Polish Academy of Sciences(波兰科学院);Warsaw University of Technology(华沙理工大学);Nicolaus Copernicus University(哥白尼大学)

Konrad Furmańczyk, Jan Mielniczuk, Wojciech Rejchel, Paweł Teisseyre

AI总结:

本文针对有偏正样本-无标签学习问题,突破SCAR常数倾向假设,提出联合最大似然与交替最大化两种双重逻辑回归估计方法,实验证明其性能优于或可比于现有EM方法。

摘要:

正样本与无标签学习是许多应用中自然产生的重要问题。几乎所有现有方法的显著局限在于假设倾向得分函数为常数(SCAR假设),这在许多实际情形中并不现实。为避免这一假设,我们考虑对后验概率函数与倾向得分函数进行联合估计的参数化方法。我们证明,在温和假设下,当两个函数具有相同的参数形式(例如参数不同的逻辑函数)时,相应参数是可识别的。受此启发,我们提出两种估计方法:联合最大似然方法,以及基于交替最大化两个Fisher一致表达式的第二种方法。我们的实验结果表明,所提方法与基于期望最大化方案的现有方法相比具有可比性或更优。

英文摘要:

Positive and unlabelled learning is an important problem which arises naturally in many applications. The significant limitation of almost all existing methods lies in assuming that the propensity score function is constant (SCAR assumption), which is unrealistic in many practical situations. Avoiding this assumption, we consider parametric approach to the problem of joint estimation of posterior probability and propensity score functions. We show that under mild assumptions when both functions have the same parametric form (e.g. logistic with different parameters) the corresponding parameters are identifiable. Motivated by this, we propose two approaches to their estimation: joint maximum likelihood method and the second approach based on alternating maximization of two Fisher consistent expressions. Our experimental results show that the proposed methods are comparable or better than the existing methods based on Expectation-Maximisation scheme.

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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