A1334
Title: Moment constrained cutting feedback for modular Bayesian models
Authors: Pushkar Kale - National University of Singapore (Singapore) [presenting]
David Nott - National University of Singapore (Singapore)
Ajay Jasra - The Chinese University of Hong Kong Shenzhen (China)
Xin Tong - National University of Singapore (Singapore)
Abstract: Statistical models are often constructed from multiple linked submodels (modules), each informed by different data sources and domain expertise. Misspecification in any module can distort posterior inference and propagate across the entire model. Cutting feedback methods address this by modifying the joint posterior so unreliable modules cannot distort inference in trusted components. The standard formulation finds the Kullback-Leibler closest distribution to the full posterior whose marginal for the shared parameters matches the posterior from the trusted module alone. However, sampling from this posterior is challenging because it requires evaluating an intractable marginal density at each step. Consequently, naive nested MCMC is typically used, leading to high computational cost. An alternative formulation, called the moment-constrained cut (MCC) posterior, replaces the full distributional constraint with a finite set of marginal mean and variance constraints on the shared parameters. The resulting distribution admits an exponential tilting representation, with the tilting coefficients estimated via stochastic gradient descent coupled with MCMC updates, whose convergence properties are established theoretically. This eliminates the need to run a separate Markov chain for each sample. Three benchmark examples demonstrate that the MCC posterior produces results similar to the conventional cut posterior while being much easier to compute.
