论文标题
从总数据中学习随机行为
Learning Stochastic Behaviour from Aggregate Data
论文作者
论文摘要
从汇总数据中学习非线性动力学是一个具有挑战性的问题，因为每个人都不可用的整个轨迹，也就是说，在下一个时间点可能不会观察到的个体，或者个人的身份不可用。这与使用完整的轨迹数据的学习动态形成了鲜明的对比，大多数现有方法都基于该数据。我们提出了一种新的方法，使用弱形式的Fokker Planck方程（FPE）（一种部分微分方程）来描述以采样形式描述数据的密度演化，然后将其与训练过程中的Wasserstein生成对抗网络（WGAN）相结合。在这样的基于样本的框架中，我们能够从聚合数据中学习非线性动力学，而无需明确求解偏微分方程（PDE）FPE。我们在一系列合成和现实世界数据集的背景下演示了我们的方法。
Learning nonlinear dynamics from aggregate data is a challenging problem because the full trajectory of each individual is not available, namely, the individual observed at one time may not be observed at the next time point, or the identity of individual is unavailable. This is in sharp contrast to learning dynamics with full trajectory data, on which the majority of existing methods are based. We propose a novel method using the weak form of Fokker Planck Equation (FPE) -- a partial differential equation -- to describe the density evolution of data in a sampled form, which is then combined with Wasserstein generative adversarial network (WGAN) in the training process. In such a sample-based framework we are able to learn the nonlinear dynamics from aggregate data without explicitly solving the partial differential equation (PDE) FPE. We demonstrate our approach in the context of a series of synthetic and real-world data sets.
