Maximum Entropy Relaxation of Multi-Way Cardinality Constraints for Synthetic Population Generation

2026-03-23

AI Summary

This work addresses the challenge of synthetic population generation under numerous high-order (e.g., three-way) multi-way marginal constraints, a setting where combinatorial explosion severely limits scalability. The authors introduce, for the first time, the principle of maximum entropy to this problem by relaxing hard constraints into moment-matching expectations, thereby formulating a synthetic population distribution within the exponential family. Through Lagrangian duality, the resulting inference task is transformed into a convex optimization problem that can be solved efficiently. Compared to conventional iterative proportional fitting approaches—such as generalized raking—the proposed method demonstrates markedly improved scalability and numerical stability. Empirical evaluations on the NPORS benchmark (with 4–40 attributes) show consistent superiority even as the number of attributes and higher-order interactions increases, effectively overcoming the longstanding trade-off between representational expressiveness and computational efficiency in existing methods.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Generating synthetic populations from aggregate statistics is a core component of microsimulation, agent-based modeling, policy analysis, and privacy-preserving data release. Beyond classical census marginals, many applications require matching heterogeneous unary, binary, and ternary constraints derived from surveys, expert knowledge, or automatically extracted descriptions. Constructing populations that satisfy such multi-way constraints simultaneously poses a significant computational challenge. We consider populations where each individual is described by categorical attributes and the target is a collection of global frequency constraints over attribute combinations. Exact formulations scale poorly as the number and arity of constraints increase, especially when the constraints are numerous and overlapping. Grounded in methods from statistical physics, we propose a maximum-entropy relaxation of this problem. Multi-way cardinality constraints are matched in expectation rather than exactly, yielding an exponential-family distribution over complete population assignments and a convex optimization problem over Lagrange multipliers. We evaluate the approach on NPORS-derived scaling benchmarks with 4 to 40 attributes and compare it primarily against generalized raking. The results show that MaxEnt becomes increasingly advantageous as the number of attributes and ternary interactions grows, while raking remains competitive on smaller, lower-arity instances.

Problem

• synthetic population generation
• multi-way cardinality constraints
• maximum entropy
• microsimulation
• constraint satisfaction

Innovation

• maximum entropy
• synthetic population generation
• multi-way constraints
• convex optimization
• exponential-family distribution