Learning to Match via Inverse Optimal Transport
Learning to Match via Inverse Optimal Transport
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发表时间：
2018-02
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通讯作者：
Ruilin Li;X. Ye;Haomin Zhou;H. Zha
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作者：
Ruilin Li;X. Ye;Haomin Zhou;H. Zha
我们提出了一个统一的数据驱动框架的基础上逆最优运输，可以学习自适应，非线性交互成本函数的噪声和不完整的经验匹配矩阵和预测新的匹配在各种匹配的上下文中。我们强调，离散的最佳运输起着变分原理的作用，从而产生了一个基于优化的框架来模拟所观察到的经验匹配数据。我们的配方导致一个非凸优化问题，可以有效地解决交替优化方法。我们制定的一个关键的新方面是通过正则化Wasserstein距离纳入边缘松弛，显着提高了该方法在面对噪声或丢失的经验匹配数据的鲁棒性。我们的模型福尔斯属于规定性模型的范畴，它不仅预测潜在的未来匹配，但也能够解释是什么导致经验匹配和量化的匹配因素的变化的影响。所提出的方法具有广泛的适用性，包括预测匹配在线约会，劳动力市场，大学申请和众包。我们支持我们的索赔与数值实验的合成数据和真实的世界数据集。
We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching contexts. We emphasize that the discrete optimal transport plays the role of a variational principle which gives rise to an optimization-based framework for modeling the observed empirical matching data. Our formulation leads to a non-convex optimization problem which can be solved efficiently by an alternating optimization method. A key novel aspect of our formulation is the incorporation of marginal relaxation via regularized Wasserstein distance, significantly improving the robustness of the method in the face of noisy or missing empirical matching data. Our model falls into the category of prescriptive models, which not only predict potential future matching, but is also able to explain what leads to empirical matching and quantifies the impact of changes in matching factors. The proposed approach has wide applicability including predicting matching in online dating, labor market, college application and crowdsourcing. We back up our claims with numerical experiments on both synthetic data and real world data sets.