Blindness of score-based methods to isolated components and mixing proportions
This highlights a critical practical limitation for researchers and practitioners using score-based methods in density estimation and Bayesian inference, though it is an incremental analysis of existing methods.
The paper identifies that score-based methods, such as score matching, fail to discover isolated components or identify correct mixing proportions in unnormalized distributions, despite their theoretical guarantees, as demonstrated through simple examples.
Statistical tasks such as density estimation and approximate Bayesian inference often involve densities with unknown normalising constants. Score-based methods, including score matching, are popular techniques as they are free of normalising constants. Although these methods enjoy theoretical guarantees, a little-known fact is that they exhibit practical failure modes when the unnormalised distribution of interest has isolated components -- they cannot discover isolated components or identify the correct mixing proportions between components. We demonstrate these findings using simple distributions and present heuristic attempts to address these issues. We hope to bring the attention of theoreticians and practitioners to these issues when developing new algorithms and applications.