Robustness of Neural Ratio and Posterior Estimators to Distributional Shifts for Population-level Dark Matter Analysis in Strong Gravitational Lensing

We investigate the robustness of neural ratio estimators (NREs) and sequential neural posterior estimators (SNPEs) to distributional shifts in the context of measuring the abundance of dark matter subhalos using strong gravitational lensing data. While these data-driven inference frameworks can be accurate on test data from the same distribution as the training sets, in real applications, it is expected that simulated training data and true observational data will differ in their distributions. We explore the behavior of a trained NRE and trained SNPEs to estimate the population-level parameters of dark matter subhalos from a large sample of images of strongly lensed galaxies with test data presenting distributional shifts within and beyond the bounds of the training distribution in the nuisance parameters (e.g., the background source morphology). While our results show that NREs and SNPEs perform well when tested perfectly in distribution, they exhibit significant biases that often lead to not recovering the ground truth in the 3σ interval when confronted with slight deviations from the examples seen in the training distribution. This indicates the necessity for caution when applying NREs and SNPEs to real astrophysical data, where high-dimensional underlying distributions are not perfectly known.