Learning General Gaussian Mixtures With Efficient Score Matching
0Vasilis Kontonis (UT Austin)
https://simons.berkeley.edu/talks/vasilis-kontonis-ut-austin-2024-11-20
Joint IFML/MPG Symposium
Our approach departs from commonly used techniques for this problem like the method of moments. Instead, we leverage a recently developed reduction, based on diffusion models, from distribution learning to a supervised learning task called score matching. We give an algorithm for the latter by proving a structural result showing that the score function of a Gaussian mixture can be approximated by a piecewise-polynomial function, and there is an efficient algorithm for finding it. To our knowledge, this is the first example of diffusion models achieving a state-of-the-art theoretical guarantee for an unsupervised learning task.