Invariant Distribution

Invariant distributions, probability distributions unchanged by specific transformations, are a central focus in various fields, with research aiming to efficiently sample from, certify the existence of, and leverage these distributions for improved model performance. Current efforts concentrate on developing novel algorithms, such as weak generative samplers and sum-of-squares methods, to address the challenges of sampling and verifying invariance in high-dimensional spaces, particularly for non-Gaussian distributions. This research is crucial for advancing machine learning, particularly in areas like robust statistics and graph generation, by enabling the development of more efficient and reliable models that account for inherent symmetries in data.