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 exact-enumeration approaches is expectation computation by explicit summation over the full tuple space $\cX$, which becomes infeasible for more than $K \approx 20$ categorical attributes; sampling-based alternatives exist but rely on Metropolis-type schemes that require proposal tuning and rejection steps. 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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2603.27312 [cs.LG] |
| (or arXiv:2603.27312v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2603.27312 arXiv-issued DOI via DataCite |
From: Mirko Degli Esposti [view email]
[v1]
Sat, 28 Mar 2026 15:36:20 UTC (829 KB)
[v2]
Fri, 17 Apr 2026 09:49:12 UTC (829 KB)
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