Science · Benchmarks
A publicly documented protocol, reproducible by third parties.
Maximum Entropy Relaxation is compared with generalized raking under a common protocol based on NPORS-derived data, with 4 to 40 attributes and different levels of constraints.
Publication: ArXiv:2603.22558 — Status: Preprint · not peer reviewed
What happens as complexity increases?
The benchmark does not seek to establish that one method is inherently better. It observes how two methods behave as the number of simultaneous attributes and the arity of constraints increase.
What is compared, and on which data.
| Method evaluated | Maximum Entropy Relaxation |
|---|---|
| Reference method | generalized raking |
| Data | NPORS-derived |
| Attributes | 4 to 40 |
| Constraints | unary, binary, ternary |
SourceFrançois Pachet, Jean-Daniel Zucker — Maximum Entropy Relaxation of Multi-Way Cardinality Constraints for Synthetic Population Generation, ArXiv, April 2026 (preprint, not peer reviewed) — ArXiv:2603.22558 View
Deviations from target distributions.
The comparison variable is deviation from target distributions, read separately at the unary, binary and ternary levels rather than aggregated into a single indicator.
K ≥ 28.
In this protocol, from 28 attributes onward in the presence of ternary constraints, Maximum Entropy Relaxation achieves better results according to the selected metric.
Summary reading of the published result. Detailed values are provided in the preprint. No measurement point is reconstructed on this page.
A threshold, not general superiority.
Below this threshold, the two methods remain comparable according to the same metric. The result describes a dependence on complexity, not an absolute ranking. It applies to the protocol described in the preprint and to this metric.
Limit of this result
What this benchmark does not validate.
- This benchmark validates only the behavior observed under this protocol.
- It validates neither every configuration, nor every dataset, nor the behavioral conclusions of simulations.
Maximum Entropy Relaxation of Multi-Way Cardinality Constraints for Synthetic Population Generation
François Pachet · Jean-Daniel Zucker
ArXiv:2603.22558 — April 2026
Preprint — not peer reviewed
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