Astronomy has undergone a profound transformation in recent years, as the acquisition of ever-growing amounts of data through increasingly powerful instruments has opened up a wealth of new avenues of exploration. However, this boon is not without its own set of challenges, as astronomical observations are often multi-dimensional in nature, encompassing the most meticulous imaging of weak lensing, reionization, and protoplanetary disks at their finest details, as well as the comprehensive characterization of complex galaxy mergers throughout cosmic history. In this realm, conventional astrostatistical methods falter.
To address this challenge, I will expound upon two different machine-learning approaches for characterizing these complex astronomical systems. Firstly, the Mathematics of Information: I will explore how machine learning can refine the compression of information and extract higher-order moments in stochastic processes. Secondly, a Generative Paradigm: I will delve into how generative models, such as normalizing flows and diffusion models, permit us to model astronomical data sets with exactitude, furthering the study of complicated astronomical systems within their observational domain.
