Reproduce “Efficient Deconvolution in Populational Inverse Problems” on OpenResearch

About this paper

Arnaud Vadeboncoeur, Mark Girolami, Andrew M. Stuart

A unified framework concurrently addresses blind deconvolution and distributional inverse problems, inferring both model parameter distributions and unknown observational noise distributions from population data. It employs an active learning scheme for surrogate models and a robust cut-gradient optimization, demonstrating accurate parameter and noise estimation with low errors across complex physical systems like porous media and chaotic dynamics.

Key insights

• The cut-gradient approach provides more stable and accurate estimation of noise parameters from finite empirical data compared to standard gradient methods, especially when the noise distribution influences the metric itself.
• Concurrent learning of an adaptive surrogate model that focuses on high-density regions of the inferred parameter distribution dramatically reduces the computational burden of complex physical models, making otherwise intractable inference problems feasible.
• By appropriately formulating the loss with a Sliced-Wasserstein metric weighted by the unknown noise covariance, it is possible to deconvolve the unknown noise distribution simultaneously with inferring the population parameter distribution.

Summary by alphaXiv.