Learning Mixtures of Random Utility Models
Learning Mixtures of Random Utility Models
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DOI：
10.1609/aaai.v32i1.11727
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
Zhibing Zhao;Tristan Villamil;Lirong Xia
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文献类型：
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作者：
Zhibing Zhao;Tristan Villamil;Lirong Xia
我们解决了随机效用模型的识别和有效学习的问题（朗姆酒）。替代方案M≥2K-1。基于EM的算法，我们称之为E-GMM，一种直接的普遍使用词法（GMM）算法，以及一种结合了其他两个实验的三明治（GMM-E-GMM）算法。三明治算法达到最高的统计效率，而GMM是最有效的，在Preflib的现实世界中实验表明，高斯K-Rums比单个高斯提供了更好的健身朗姆酒，Plackett-luce模型和Plackett-luce模型W.R.T.通常是我们所知的通用模型适应性标准。
We tackle the problem of identifiability and efficient learning of mixtures of Random Utility Models (RUMs). We show that when the PDFs of utility distributions are symmetric, the mixture of k RUMs (denoted by k-RUM) is not identifiable when the number of alternatives m is no more than 2k-1. On the other hand, when m ≥ max{4k-2,6}, any k-RUM is generically identifiable. We then propose three algorithms for learning mixtures of RUMs: an EM-based algorithm, which we call E-GMM, a direct generalized-method-of-moments (GMM) algorithm, and a sandwich (GMM-E-GMM) algorithm that combines the other two. Experiments on synthetic data show that the sandwich algorithm achieves the highest statistical efficiency and GMM is the most computationally efficient. Experiments on real-world data at Preflib show that Gaussian k-RUMs provide better fitness than a single Gaussian RUM, the Plackett-Luce model, and mixtures of Plackett-Luce models w.r.t. commonly-used model fitness criteria. To the best of our knowledge, this is the first work on learning mixtures of general RUMs.