Learning Iterative Updates to Sampling Distributions from Density-Ratio Feedback

Generative models enable inference from incomplete observations by sampling plausible underlying structures from learned distributions. However, a mismatch between the sampling distribution and the target posterior can leave regions with substantial posterior probability represented by only a few samples. Such mismatch can increase posterior-mean estimation error under a fixed number of target density evaluations. In this work, we introduce the Ratio-Guided Proposal Compiler (RGPC), a learned model that iteratively updates the sampling distribution to reduce distribution mismatch and posterior-mean estimation error. To guide these updates, RGPC compares the density of the target posterior with the current sampling density at trial samples, then combines the resulting density-ratio feedback with aggregate constraints to predict changes to the sampling distribution's parameters. Across 32 Public Use Microdata Areas (PUMAs), we evaluate population inference on development tasks defined by subsets of American Community Survey (ACS) aggregate statistics, with all methods approximating the same target posterior for each task. We measure distribution mismatch using squared maximum mean discrepancy (${\mathrm{MMD}}^2$), which compares distributions through their samples. For posterior-mean estimation error, we use total variation distance (TVD) between the estimated and reference posterior means. RGPC achieves the lowest ${\mathrm{MMD}}^2$ and TVD among all nine evaluated methods, including conditional generators and conventional sampling baselines. When using the same number of target density evaluations, RGPC reduces ${\mathrm{MMD}}^2$ by 42.65% and TVD by 26.50% relative to the best-performing baseline. Code is available at https://anonymous.4open.science/r/RGPC-FD4B/.