论文标题
带有到达建模和模拟中应用的双随机模拟器
A Doubly Stochastic Simulator with Applications in Arrivals Modeling and Simulation
论文作者
论文摘要
我们提出了一个框架，该框架集成了经典的蒙特卡洛模拟器和Wasserstein生成的对抗网络，以建模，估算和模拟一类广泛的到达过程，并具有一般的非平稳和多维随机到达率。经典的蒙特卡洛模拟器在捕获随机物体的可解释的“物理”方面具有优势，而基于神经网络的模拟器具有捕获高维分布中可隔离较小的复杂依赖性的优势。我们提出了一个双重的随机模拟器，该模拟器整合了随机生成神经网络和经典的蒙特卡洛泊松模拟器，以利用这两个优势。这种集成给定数据估算的理论可靠性和计算障碍带来了挑战，在给定的真实数据中，估计是通过最大程度地减少模拟输出的分布与真实数据分布之间的瓦斯恒星距离来完成的。关于理论特性，我们证明在非参数平滑度假设下，估计的模拟器的一致性和收敛速率。关于估计程序的计算效率和障碍性，我们解决了梯度评估中的挑战，该挑战是由蒙特卡洛泊松模拟器中的不连续性引起的。实施了合成和实际数据集的数值实验，以说明所提出的框架的性能。
We propose a framework that integrates classical Monte Carlo simulators and Wasserstein generative adversarial networks to model, estimate, and simulate a broad class of arrival processes with general non-stationary and multi-dimensional random arrival rates. Classical Monte Carlo simulators have advantages at capturing the interpretable "physics" of a stochastic object, whereas neural-network-based simulators have advantages at capturing less-interpretable complicated dependence within a high-dimensional distribution. We propose a doubly stochastic simulator that integrates a stochastic generative neural network and a classical Monte Carlo Poisson simulator, to utilize both advantages. Such integration brings challenges to both theoretical reliability and computational tractability for the estimation of the simulator given real data, where the estimation is done through minimizing the Wasserstein distance between the distribution of the simulation output and the distribution of real data. Regarding theoretical properties, we prove consistency and convergence rate for the estimated simulator under a non-parametric smoothness assumption. Regarding computational efficiency and tractability for the estimation procedure, we address a challenge in gradient evaluation that arise from the discontinuity in the Monte Carlo Poisson simulator. Numerical experiments with synthetic and real data sets are implemented to illustrate the performance of the proposed framework.
