Nonuniform Negative Sampling and Log Odds Correction with Rare Events Data
Nonuniform Negative Sampling and Log Odds Correction with Rare Events Data
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发表时间：
2021-10
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通讯作者：
HaiYing Wang;Aonan Zhang;Chong Wang
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作者：
HaiYing Wang;Aonan Zhang;Chong Wang
研究了不平衡数据的非均匀负抽样参数估计问题。我们首先证明，对于不平衡的数据，关于未知参数的可用信息仅与相对较少的正实例相关联，这证明了负抽样的使用是合理的。然而，如果负面实例被抽样到与正面实例相同的水平，就会有信息丢失。为了保持更多的信息，我们推导了一般逆概率加权（IPW）估计量的渐近分布，并得到了使其方差最小的最优抽样概率。为了进一步提高IPW方法的估计效率，我们提出了一个基于似然的估计量，通过对采样数据的对数赔率进行校正，并证明了改进的估计量在一大类估计量中具有最小的渐近方差。它也更健壮，以指导错误规范。我们在模拟数据和真实点击率数据集上验证了我们的方法，这些数据集在一个月内收集了超过0.3万亿个实例。理论和实证结果均证明了该方法的有效性。
We investigate the issue of parameter estimation with nonuniform negative sampling for imbalanced data. We first prove that, with imbalanced data, the available information about unknown parameters is only tied to the relatively small number of positive instances, which justifies the usage of negative sampling. However, if the negative instances are subsampled to the same level of the positive cases, there is information loss. To maintain more information, we derive the asymptotic distribution of a general inverse probability weighted (IPW) estimator and obtain the optimal sampling probability that minimizes its variance. To further improve the estimation efficiency over the IPW method, we propose a likelihood-based estimator by correcting log odds for the sampled data and prove that the improved estimator has the smallest asymptotic variance among a large class of estimators. It is also more robust to pilot misspecification. We validate our approach on simulated data as well as a real click-through rate dataset with more than 0.3 trillion instances, collected over a period of a month. Both theoretical and empirical results demonstrate the effectiveness of our method.