BibTeX

@article{2410.19990v2,
Author        = {Ricardo Baptista and Michael Brennan and Youssef Marzouk},
Title         = {Dimension reduction via score ratio matching},
Eprint        = {2410.19990v2},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.CO},
Abstract      = {Gradient-based dimension reduction decreases the cost of Bayesian inference
and probabilistic modeling by identifying maximally informative (and informed)
low-dimensional projections of the data and parameters, allowing
high-dimensional problems to be reformulated as cheaper low-dimensional
problems. A broad family of such techniques identify these projections and
provide error bounds on the resulting posterior approximations, via
eigendecompositions of certain diagnostic matrices. Yet these matrices require
gradients or even Hessians of the log-likelihood, excluding the purely
data-driven setting and many problems of simulation-based inference. We propose
a framework, derived from score-matching, to extend gradient-based dimension
reduction to problems where gradients are unavailable. Specifically, we
formulate an objective function to directly learn the score ratio function
needed to compute the diagnostic matrices, propose a tailored parameterization
for the score ratio network, and introduce regularization methods that
capitalize on the hypothesized low-dimensional structure. We also introduce a
novel algorithm to iteratively identify the low-dimensional reduced basis
vectors more accurately with limited data based on eigenvalue deflation
methods. We show that our approach outperforms standard score-matching for
problems with low-dimensional structure, and demonstrate its effectiveness for
PDE-constrained Bayesian inverse problems and conditional generative modeling.},
Year          = {2024},
Month         = {Oct},
Url           = {http://arxiv.org/abs/2410.19990v2},
File          = {2410.19990v2.pdf}
}