Covid19 Reproduction Number: Credibility Intervals by Blockwise Proximal Monte Carlo Samplers

Monitoring the Covid19 pandemic constitutes a critical societal stake that received considerable research efforts. The intensity of the pandemic on a given territory is efficiently measured by the reproduction number, quantifying the rate of growth of daily new infections. Recently, estimates for the time evolution of the reproduction number were produced using an inverse problem formulation with a nonsmooth functional minimization. While it was designed to be robust to the limited quality of the Covid19 data (outliers, missing counts), the procedure lacks the ability to output credibility interval based estimates. This remains a severe limitation for practical use in actual pandemic monitoring by epidemiologists that the present work aims to overcome by use of Monte Carlo sampling. After interpretation of the nonsmooth functional into a Bayesian framework, several sampling schemes are tailored to adjust the nonsmooth nature of the resulting posterior distribution. The originality of the devised algorithms stems from combining a Langevin Monte Carlo sampling scheme with Proximal operators. Performance of the new algorithms in producing relevant credibility intervals for the reproduction number estimates and denoised counts are compared. Assessment is conducted on real daily new infection counts made available by the Johns Hopkins University. The interest of the devised monitoring tools are illustrated on Covid19 data from several different countries. IEEE

Improving Effectiveness of Simulation-Based Inference in the Massively Parallel Regime

Simulation-based Inference (SBI) is a widely used set of algorithms to learn the parameters of complex scientific simulation models. While primarily run on CPUs in High-Performance Compute clusters, these algorithms have been shown to scale in performance when developed to be run on massively parallel architectures such as GPUs. While parallelizing existing SBI algorithms provides us with performance gains, this might not be the most efficient way to utilize the achieved parallelism. This work proposes a new parallelism-aware adaptation of an existing SBI method, namely approximate Bayesian computation with Sequential Monte Carlo(ABC-SMC). This new adaptation is designed to utilize the parallelism not only for performance gain, but also toward qualitative benefits in the learnt parameters. The key idea is to replace the notion of a single ‘step-size’hyperparameter, which governs how the state space of parameters is explored during learning, with step-sizes sampled from a tuned Beta distribution. This allows this new ABC-SMC algorithm to more efficiently explore the state-space of the parameters being learned. We test the effectiveness of the proposed algorithm to learn parameters for an epidemiology model running on a Tesla T4 GPU. Compared to the parallelized state-of-the-art SBI algorithm, we get similar quality results in <inline-formula><tex-math notation="LaTeX">$\sim 100 \times$</tex-math></inline-formula> fewer simulations and observe <inline-formula><tex-math notation="LaTeX">$\sim 80 \times$</tex-math></inline-formula> lower run-to-run variance across 10 independent trials. IEEE