Understanding the Spread of COVID-19 Epidemic: A Spatio-Temporal Point Process View

Since the first coronavirus case was identified in the U.S. on Jan. 21, more than 1 million people in the U.S. have confirmed cases of COVID-19. This infectious respiratory disease has spread rapidly across more than 3000 counties and 50 states in the U.S. and have exhibited evolutionary clustering and complex triggering patterns. It is essential to understand the complex spacetime intertwined propagation of this disease so that accurate prediction or smart external intervention can be carried out. In this paper, we model the propagation of the COVID-19 as spatio-temporal point processes and propose a generative and intensity-free model to track the spread of the disease. We further adopt a generative adversarial imitation learning framework to learn the model parameters. In comparison with the traditional likelihood-based learning methods, this imitation learning framework does not need to prespecify an intensity function, which alleviates the model-misspecification. Moreover, the adversarial learning procedure bypasses the difficult-to-evaluate integral involved in the likelihood evaluation, which makes the model inference more scalable with the data and variables. We showcase the dynamic learning performance on the COVID-19 confirmed cases in the U.S. and evaluate the social distancing policy based on the learned generative model.

[1]  Peter J. Diggle,et al.  Spatio-Temporal Point Processes: Methods and Applications , 2005 .

[2]  Stefano Ermon,et al.  Generative Adversarial Imitation Learning , 2016, NIPS.

[3]  Le Song,et al.  Learning Temporal Point Processes via Reinforcement Learning , 2018, NeurIPS.

[4]  Stephen L. Rathbun,et al.  Asymptotic properties of the maximum likelihood estimator for spatio-temporal point processes , 1996 .

[5]  Alex Reinhart,et al.  A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications , 2017, Statistical Science.

[6]  J. Møller,et al.  Log Gaussian Cox Processes , 1998 .

[7]  Yoshua Bengio,et al.  Generative Adversarial Nets , 2014, NIPS.

[8]  Max Welling,et al.  Auto-Encoding Variational Bayes , 2013, ICLR.

[9]  Peter J. Diggle,et al.  Spatial and spatio-temporal Log-Gaussian Cox processes:extending the geostatistical paradigm , 2013, 1312.6536.

[10]  George E. Tita,et al.  Self-Exciting Point Process Modeling of Crime , 2011 .

[11]  Pieter Abbeel,et al.  Apprenticeship learning via inverse reinforcement learning , 2004, ICML.

[12]  V. Isham,et al.  A self-correcting point process , 1979 .

[13]  Daan Wierstra,et al.  Stochastic Backpropagation and Approximate Inference in Deep Generative Models , 2014, ICML.

[14]  J. Grandell Doubly stochastic Poisson processes , 1976 .

[15]  J. Møller,et al.  Statistical Inference and Simulation for Spatial Point Processes , 2003 .

[16]  A. Hawkes Spectra of some self-exciting and mutually exciting point processes , 1971 .

[17]  Andrew Y. Ng,et al.  Pharmacokinetics of a novel formulation of ivermectin after administration to goats , 2000, ICML.