Traditional compartmental models capture population-level dynamics but fail to characterize individual-level risk. The computational cost of exact likelihood evaluation for partially observed individual-based models, however, grows exponentially with the population size, necessitating approximate inference. Existing sampling-based methods usually require multiple simulations of the individuals in the population and rely on bespoke proposal distributions or summary statistics. We propose a deterministic approach to approximating the likelihood using categorical distributions. The approximate likelihood is amenable to automatic differentiation so that parameters can be estimated by maximization or posterior sampling using standard software libraries such as Stan or TensorFlow with little user effort. We prove the consistency of the maximum approximate likelihood estimator. We empirically test our approach on several classes of individual-based models for epidemiology: different sets of disease states, individual-specific transition rates, spatial interactions, under-reporting and misreporting. We demonstrate ground truth recovery and comparable marginal log-likelihood values at substantially reduced cost compared to competitor methods. Finally, we show the scalability and effectiveness of our approach with a real-world application on the 2001 UK Foot-and-Mouth outbreak, where the simplicity of the CAL allows us to include 162775 farms.

翻译：传统隔室模型能够捕捉群体层面的动态特征，但无法刻画个体层面的风险。然而，针对部分可观测个体化模型进行精确似然评估的计算成本会随人口规模呈指数级增长，这使得近似推断成为必然需求。现有的基于采样的方法通常需要对群体中的个体进行多次模拟，并依赖于定制化的提议分布或摘要统计量。本文提出一种利用分类分布逼近似然函数的确定性方法。该近似似然适用于自动微分，因此可通过最大化或后验采样（使用Stan或TensorFlow等标准软件库）进行参数估计，且几乎无需用户干预。我们证明了最大近似似然估计量的一致性。我们在流行病学的多类个体化模型上对所提方法进行了实证检验：这些模型涵盖不同的疾病状态集、个体特异性转移率、空间交互作用、漏报与误报情形。实验表明，相较于现有竞争方法，本方法能以显著降低的成本实现真实参数恢复，并获得可比较的边际对数似然值。最后，我们通过2001年英国口蹄疫爆发的实际案例，展示了本方法的可扩展性与有效性——得益于CAL的简洁性，我们成功将162775个农场纳入模型。