Joint Prediction of Multiple Waiting Times with Recurrent Neural Nets

需求预测对零售商来说一直很重要，因为它推动着有关商业战略和供应链管理的重要决策。传统方法使用经典统计模型对购买到达率进行建模，这些模型开发时无法轻松获取可扩展的计算能力以及广泛(多种类型的数据)和长期(对许多个人而言)的购买数据。近年来海量数据带来的好处不应该局限于更好地估计总体统计数据来应用经典统计模型，还应该包括基于详细的个人级别购买信息的更细粒度的建模。经典统计中已经提出了许多模型来描述事件到达的行为，因为它们在许多领域都很有用，如监测设备剩余寿命和灾害预测。这些模型都经过了细致的描述，它们的特性也得到了严格的证明。然而，这些相同的模型也需要大量的假设，这些假设在现实中可能不一定成立。一个这样的假设是，在时间上相隔较远的事件之间的相关性也往往较小。我们希望探索一种旨在放松这些假设的数据驱动模型。最近计算能力的爆炸性增长重新点燃了人们对人工神经网络的兴趣，它已经在许多不同的应用领域取得了成功。对其进行修改的是递归神经网络。随着内部状态变量的增加，这种神经网络设置也可以应用于顺序数据。它还被证明是图灵完全的，这意味着它可以在给定足够大的参数集的情况下模拟任何计算机程序。RNN在自然语言处理中的应用已经取得了相当的成功，表明该模型在捕捉复杂顺序依赖方面比经典统计模型要好得多，因为经典模型需要短程依赖假设。

Demand forecasting has always been important for retailers as it drives important decisions regarding businessstrategy and supply chain management. Traditional approaches model the purchase arrival rates using classicalstatistical models, which were developed without easy access to scalable computing power and both wide(many types of data) and long (for many individuals) purchase data. Benefits brought forth by the huge influxof data during the recent years ought not to be limited to having better estimates of aggregate statistics to applyclassical statistical models, but should also include a more fine-grained modelling based on the detailedindividual-level purchase information.There have been many models proposed in classical statistics to describe the behaviour of event arrivals, asthey're useful in many areas, such as monitoring equipment remaining lifetimes and disaster forecasting. Thesemodels have been meticulously described and their properties have been rigorously proven. However, thesesame models also require a large number of assumptions, which may not necessarily hold in reality. One suchassumption is that the dependence between events occurring further apart in time also tends to be smaller. We'dlike to explore a data-driven model that aims to relax these assumptions. The recent explosion in accessibilityto computational power has re-ignited interest in the Artificial Neural Net, which has shown success in manydifferent areas of application. A modification to this is the Recurrent Neural Net. With the addition of aninternal state variable, this neural-network set-up can be applied to sequential data as well. It had also beenshown to be Turing complete, meaning that it can emulate any computer program given a large enough set ofparameters. Applications of the RNN in natural language processing have been rather successful,demonstrating that this model is much better than classical statistical models in capturing complex sequentialdependence, since the classical models require short-range dependence assumptions to work.