用于估算商业设施收入和需求的变分贝叶斯空间相互作用模型
A variational Bayesian spatial interaction model for estimating revenue and demand at business facilities
摘要：
我们研究的问题，估计潜在的收入或需求在业务设施和理解其生成机制。这个问题出现在不同的领域，如运筹学或城市科学，更普遍的是，它对企业的规划和决策至关重要。我们开发了一个贝叶斯空间相互作用模型，此后BSIM，它提供了一个特定的业务位置提供他们的功能和潜在客户的特性在给定的区域所产生的收入的概率预测。BSIM明确占竞争力的设施之间的竞争，通过一个概率值，通过评估一个商店特定的高斯分布在一个给定的客户位置。我们提出了一个可扩展的变分推断框架，而明显快于竞争马尔可夫链蒙特卡罗推理计划，具有可比的性能参数识别和不确定性量化。我们展示了BSIM在各种综合环境中的优势，其特点是商店和客户数量不断增加。最后，我们构建了一个真实世界的大型空间数据集，用于英国伦敦的酒吧活动，其中包括超过1，500家酒吧和150，000个客户区域。我们展示了BSIM在预测性能方面如何在这个大型数据集上优于竞争方法，同时提供可解释的结果，并与伦敦地区观察到的相关指标一致。
英文摘要：
We study the problem of estimating potential revenue or demand at business facilities and understanding its generating mechanism. This problem arises in different fields such as operation research or urban science, and more generally, it is crucial for businesses' planning and decision making. We develop a Bayesian spatial interaction model, henceforth BSIM, which provides probabilistic predictions about revenues generated by a particular business location provided their features and the potential customers' characteristics in a given region. BSIM explicitly accounts for the competition among the competitive facilities through a probability value determined by evaluating a store-specific Gaussian distribution at a given customer location. We propose a scalable variational inference framework that, while being significantly faster than competing Markov Chain Monte Carlo inference schemes, exhibits comparable performances in terms of parameters identification and uncertainty quantification. We demonstrate the benefits of BSIM in various synthetic settings characterised by an increasing number of stores and customers. Finally, we construct a real-world, large spatial dataset for pub activities in London, UK, which includes over 1,500 pubs and 150,000 customer regions. We demonstrate how BSIM outperforms competing approaches on this large dataset in terms of prediction performances while providing results that are both interpretable and consistent with related indicators observed for the London region.
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