利用Mallows-φ模型的不完整序数偏好预测

Prediction of Incomplete Ordinal Preference Based on Mallows-φModel

序数偏好可解决用户评价准则不一致的问题,在社会选择、在线服务信誉度量、推荐系统等领域中发挥着重要的作用.然而,由于用户认知能力和隐私等原因,通常难以获得用户的完整序数偏好.基于不完整偏好进行目标选择、在线服务信誉度量、产品推荐等决策时,难以保证决策结果的有效性和准确性.考虑到成对比较是一种常见的用户序数偏好表达形式,提出了一种对缺失成对比较序数偏好进行预测的方法.首先,使用不完整成对比较序数偏好训练Mallows-φ排名模型;然后,使用训练得到的模型对指定用户可能的完整偏好进行采样,每个采样的完整偏好都满足该用户不完整偏好中优先关系的约束;最后,使用采样的完整偏好对用户缺失的成对比较进行预测.基于真实数据和人工合成数据的实验结果表明,在用户偏好缺失率不超过70%时,方法可以对缺失偏好进行准确的预测.

Ordinal preference can solve the problem of inconsistent user evaluation criteria,and plays an important role in social selection,online service reputation measurement,recommendation systems and other fields.However,due to reasons such as user cognitive ability and privacy,it is usually difficult to obtain the user′s complete ordinal preference.When making decisions based on incomplete preferences,such as target selection,online service reputation measurement,product recommendation,etc.,it is difficult to guarantee the validity and accuracy of the decision results.Considering that pairwise comparison is a common form of user ordinal preference expression,a method for predicting missing pairwise comparison ordinal preference is proposed.First,use the incomplete pairwise comparison ordinal preference to train the Mallows-φranking model;then,use the trained model to sample the possible complete preferences of the specified user,and each sampled complete preference satisfies the priority relationship of the user′s incomplete preference;finally,use the sampled complete preferences to predict the user′s missing pairwise comparisons.Experimental results based on real data and artificially synthesized data show that the method can accurately predict the missing preferences when the user preference missing rate does not exceed 70%.