Recent advancements in astronomical instrumentation have led to an unprecedented influx of data, revolutionizing the field. However, the inherent complexity and multi-dimensionality of astronomical observations, ranging from intricate imaging of weak lensing, reionization, and protoplanetary disks to the comprehensive analysis of galaxy mergers across cosmic history, pose significant challenges to traditional astrostatistical methods.

In this colloquium, Dr. Yuan-Sen discusses two distinct machine learning approaches to tackle these complex astronomical systems. First, he explores the Mathematics of Information, focusing on how machine learning can optimize information compression and extract higher-order moments in stochastic processes.

Second, he introduces a Generative AI paradigm, demonstrating how generative models, such as normalizing flows and diffusion models, enable precise modeling of astronomical datasets, thereby facilitating accurate inference about intricate astronomical systems.

By leveraging these cutting-edge machine learning techniques, we can transcend the limitations of conventional astrostatistics and make more robust inferences about complex astronomical systems.