Scalable Maximum Entropy Population Synthesis via Persistent Contrastive Divergence

• URL: http://arxiv.org/abs/2603.27312v1
• Date: Sat, 28 Mar 2026 15:36:20 GMT
• Title: Scalable Maximum Entropy Population Synthesis via Persistent Contrastive Divergence
• Abstract summary: A principled framework for generating synthetic populations from aggregate census data is presented.<n>GibbsPCDr produces populations with effective sample size versus $Neff approx 0.012, raking an $86.8times$ diversity advantage that is essential for agent-based urban simulations.<n>GibbsPCDr maintains $MRE in [0.010, 0.018]$ while $|cX|$ grows eighteen orders of magnitude, with scaling as $O(K)$ rather than $O(cX)$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 existing approaches is exact expectation computation, which requires summing over the full tuple space $\cX$ and becomes infeasible for more than $K \approx 20$ categorical attributes. We propose \emph{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 \emph{Syn-ISTAT}, a $K{=}15$ Italian demographic benchmark with analytically exact marginal targets derived from ISTAT-inspired conditional probability tables. Scaling experiments across $K \in \{12, 20, 30, 40, 50\}$ confirm that GibbsPCDSolver maintains $\MRE \in [0.010, 0.018]$ 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 $\Neff \approx 0.012\,N$ for generalised raking, an $86.8{\times}$ diversity advantage that is essential for agent-based urban simulations.

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