Inference for high-dimensional hidden Markov models is challenging due to the exponential-in-dimension computational cost of the forward algorithm. To address this issue, we introduce an innovative composite likelihood approach called "Simulation Based Composite Likelihood" (SimBa-CL). With SimBa-CL, we approximate the likelihood by the product of its marginals, which we estimate using Monte Carlo sampling. In a similar vein to approximate Bayesian computation (ABC), SimBa-CL requires multiple simulations from the model, but, in contrast to ABC, it provides a likelihood approximation that guides the optimization of the parameters. Leveraging automatic differentiation libraries, it is simple to calculate gradients and Hessians to not only speed-up optimization, but also to build approximate confidence sets. We conclude with an extensive experimental section, where we empirically validate our theoretical results, conduct a comparative analysis with SMC, and apply SimBa-CL to real-world Aphtovirus data.

翻译：高维隐马尔可夫模型的推断面临挑战，这是由于前向算法的计算成本随维度呈指数增长。为解决该问题，我们提出了一种创新性的复合似然方法，称为“基于模拟的复合似然”（SimBa-CL）。通过SimBa-CL，我们利用蒙特卡洛采样估计各边缘分布的乘积来近似似然函数。与近似贝叶斯计算（ABC）类似，SimBa-CL需要从模型进行多次模拟，但与ABC不同的是，该方法提供了一种能够指导参数优化的似然近似。借助自动微分库，我们可以简便地计算梯度和黑塞矩阵，这不仅加速了优化过程，还能构建近似的置信集。最后，我们通过大量实验验证理论结果、与序贯蒙特卡洛（SMC）进行对比分析，并将SimBa-CL应用于真实的Aphtovirus数据。