Composite Marginal Likelihood Methods for Random Utility Models
Composite Marginal Likelihood Methods for Random Utility Models
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发表时间：
2018-06
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通讯作者：
Zhibing Zhao;Lirong Xia
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作者：
Zhibing Zhao;Lirong Xia
我们提出了一种新颖灵活的学习随机实用新型（RBCML）框架，其中包括Plackett-Luce模型。通过证明RBCML目标函数在卷积和边缘下保持严格对数凹性，刻画了RBCML目标函数是严格对数凹的条件。刻画了RBCML满足一致性和渐近正态性的充分必要条件。在合成数据上的实验表明，RBCML用于高斯rms的统计效率和计算效率比目前最先进的算法更好，我们的RBCML用于Plackett-Luce模型在运行时间和统计效率之间提供了灵活的权衡。
We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved under convolution and marginalization. We characterize necessary and sufficient conditions for RBCML to satisfy consistency and asymptotic normality. Experiments on synthetic data show that RBCML for Gaussian RUMs achieves better statistical efficiency and computational efficiency than the state-of-the-art algorithm and our RBCML for the Plackett-Luce model provides flexible tradeoffs between running time and statistical efficiency.