Scalable Maximum Entropy Population Synthesis via Persistent Contrastive Divergence

Maximum entropy (MaxEnt) modelling provides a principled framework for generating synthetic populations from aggregate census data, without access to individual-level microdata. The bottleneck of exact-enumeration approaches is expectation computation by explicit summation over the full tuple space cX, which becomes infeasible for more than K ≈ 20 categorical attributes; sampling-based alternatives exist but rely on Metropolis-type schemes that require proposal tuning and rejection steps. We propose GibbsPCDSolver, a stochastic replacement for this computation based on Persistent Contrastive Divergence (PCD): a persistent pool of N synthetic individuals is updated by Gibbs sweeps at each gradient step, providing a stochastic approximation of the model expectations without ever materialising cX. We validate the approach on controlled benchmarks and on Syn-ISTAT, a K=15 Italian demographic benchmark with analytically exact marginal targets derived from ISTAT-inspired conditional probability tables. Scaling experiments across K ∈ 12, 20, 30, 40, 50 confirm that GibbsPCDSolver maintains MRE ∈ [0.010, 0.018] while |cX| grows eighteen orders of magnitude, with runtime scaling as O(K) rather than O(|cX|). On Syn-ISTAT, GibbsPCDSolver reaches MRE=0.03 on training constraints and -- crucially -- produces populations with effective sample size Neff = N versus Neff ≈ 0.012,N for generalised raking, an 86.8× diversity advantage that is essential for agent-based urban simulations.