Improving pairwise comparison models using Empirical Bayes shrinkage
Improving pairwise comparison models using Empirical Bayes shrinkage
复制标题
使用经验贝叶斯收缩改进成对比较模型
DOI：
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发表时间：
2018
期刊：
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通讯作者：
J. Ugander
中科院分区：
文献类型：
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作者：
Stephen Ragain;A. Peysakhovich;J. Ugander
比较数据出现在许多重要的背景下，例如购物、网络点击或体育比赛。通常情况下，我们会得到一个比较数据集，并希望训练一个模型来预测看不见的比较结果。在许多情况下，可用数据集的比较相对较少（例如，每年只有这么多NFL比赛），或者效率很重要（例如，我们希望快速估计产品的相对吸引力）。在这种情况下，众所周知，收缩估计优于最大似然估计。一个复杂的问题是，标准的比较模型，如条件多项logit模型，只是条件结果（谁赢了）的模型，而不是比较本身（谁竞争了）。因此，比较过程的不同模型导致不同的收缩估计量。在这项工作中，我们推导出一个集合的方法来估计成对的不确定性的成对预测的基础上不同的假设比较过程。这些不确定性估计允许我们检查模型的不确定性以及执行模型参数的经验贝叶斯收缩估计。我们证明，对于来自在线比较调查以及几种体育背景的真实的比较数据，我们的收缩估计量优于标准最大似然方法。
Comparison data arises in many important contexts, e.g. shopping, web clicks, or sports competitions. Typically we are given a dataset of comparisons and wish to train a model to make predictions about the outcome of unseen comparisons. In many cases available datasets have relatively few comparisons (e.g. there are only so many NFL games per year) or efficiency is important (e.g. we want to quickly estimate the relative appeal of a product). In such settings it is well known that shrinkage estimators outperform maximum likelihood estimators. A complicating matter is that standard comparison models such as the conditional multinomial logit model are only models of conditional outcomes (who wins) and not of comparisons themselves (who competes). As such, different models of the comparison process lead to different shrinkage estimators. In this work we derive a collection of methods for estimating the pairwise uncertainty of pairwise predictions based on different assumptions about the comparison process. These uncertainty estimates allow us both to examine model uncertainty as well as perform Empirical Bayes shrinkage estimation of the model parameters. We demonstrate that our shrunk estimators outperform standard maximum likelihood methods on real comparison data from online comparison surveys as well as from several sports contexts.