Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations cannot be ignored and stochastic effects are important. The inference of the parameters of such models, from time series data, is difficult due to intractability of the likelihood; current methods, based on simulations of the underlying model, can be so computationally expensive as to be prohibitive. In this paper we construct a neural likelihood approximation for integer valued time series data using causal convolutions, which allows us to evaluate the likelihood of the whole time series in parallel. We demonstrate our method by performing inference on a number of ecological and epidemiological models, showing that we can accurately approximate the true posterior while achieving significant computational speed ups in situations where current methods struggle.

翻译：在物理和生物科学中，定义在整数值状态空间上的随机过程广受欢迎。这些模型对于捕捉小系统的动力学行为至关重要，因为在这些系统中，种群的个体特性不可忽略，且随机效应具有重要影响。根据时间序列数据推断此类模型的参数十分困难，原因在于似然函数的难解性；当前基于底层模型模拟的方法可能因计算成本过高而难以实施。本文利用因果卷积构建了一种针对整数值时间序列数据的神经似然逼近方法，使我们能够并行评估整个时间序列的似然函数。我们通过多个生态学和流行病学模型上的推断实验验证了该方法，结果表明：在当前方法难以应对的场景中，我们既能精确逼近真实后验分布，又能实现显著的计算加速。