Emulating cosmological likelihoods with machine learning

The process of Bayesian inference is a staple of modern science, as it allows us to learn from data in an intuitive and rigorous way. In the case of cosmology Bayesian inference is often used to turn data about astrophysical objects into estimates of cosmological parameters whose importance is paramount to un derstanding the overall structure of the universe; such an inference relies on accurately evaluating complex likelihood functions, that are often expensive to compute - requiring the use of specialized solvers. Despite the effort needed to obtain individual function values many likelihoods of cosmological relevance frequently turn out to be smooth, stable functions of their model parameters; this has led to many attempts to exploit these remarkable mathematical properties in order to skip the expensive calculations. Several software frameworks exist to allow one to approximate these functions, relying on a myriad of models, ranging from polynomial interpolation to Gaussian Processes to neural networks; yet these tools are often limited in scope, requiring the user to either stick to provenly effective use-cases or retrain the model from scratch - thus making the process of adapting likelihood emulation to new scenarios/datasets needlessly time consuming. In this work we present COSMOLIME (Cosmological LIkelihood Machine learning Emulator), a model-agnostic, self-training, machine learning-based framework to emulate arbitrary likelihood functions in a fully automated way. By providing COSMOLIME with a python function wrapping any exact likelihood solver the framework is fully autonomously able to sample points as needed and optimize the hyperparameters of an arbitrary machine learning model. This allows the user to avoid the time consuming manual process of tweaking models, checking the resulting performance, and deciding whether more simulated samples or different models altogether are needed. With many powerful features such as the caching of intermediate results, pretty logging, and options to parallelize both data generation and model optimization CosmoLIME is a tool capable of substantially innovating the current cosmological landscape, as it can provide orders of magnitude speedups in both computer and human time - thanks to the new DIY approach to emulation it offers.