  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.
