Population-Level Generative Modeling for Ranking Data

Ranking data are ubiquitous in recommendation systems, voting, and AI preference alignment. While statistical literature has focused on inferring latent preferences or predicting rankings, there is a lack of robust methods for population-level generative modeling—the ability to generate realistic, synthetic rankings that capture the heterogeneity of an observed population. This paper addresses the challenge of modeling high-dimensional, combinatorial ranking data with non-Euclidean dependence structures.

The author proposes a framework called Latent Preference Simplex Embedding (LPSE). The method operates in three steps:

1. Embedding: It represents each ranker's utility vector as a convex combination of latent utility vectors (preference types) within a low-dimensional simplex.
2. Estimation: It uses a constrained maximum likelihood estimator to estimate the latent utility matrix and then applies a vertex recovery algorithm (Successive Vertex Search) to identify the preference types.
3. Generation: It employs flow matching to learn the population distribution of the latent preference weights. New rankings are generated by sampling from this learned distribution and decoding them through a Plackett-Luce model.

The paper demonstrates that ranking generation can be reduced to an oracle problem of learning a distribution on a low-dimensional simplex. The author provides finite-sample guarantees, showing how the number of items, ranking length, and latent dimension influence the accuracy of the generative model. Experiments on both synthetic and real-world datasets confirm that the LPSE framework achieves superior population-level fidelity compared to existing methods while providing a statistically interpretable representation of preference heterogeneity.

This work bridges the gap between traditional statistical ranking models and modern generative AI. By reducing complex combinatorial objects to a low-dimensional latent space, the framework allows for privacy-preserving data sharing, robust benchmark construction, and better simulation of decision systems, all while maintaining the interpretability required for scientific and policy-oriented applications.