# Heterogeneous Ordinal Structure Learning with Bayesian Nonparametric Complexity Discovery

arXiv: https://arxiv.org/abs/2605.04191 · HTML: https://mlsanity.com/paper/2605.04191/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 10 of 10)

- [Causal Structure Discovery from Distributions Arising from Mixtures of DAGs](https://mlsanity.com/paper/2001.11940/) (2020)
- [Estimating Psychological Networks and their Accuracy: A Tutorial Paper](https://mlsanity.com/paper/1604.08462/) (2016)
- [Artificial Intelligence across Europe: A Study on Awareness, Attitude and Trust](https://mlsanity.com/paper/2308.09979/) (2023)
- [Learning Bayesian Networks from Ordinal Data](https://mlsanity.com/paper/2010.15808/) (2020)
- [Bayesian graphical modeling for heterogeneous causal effects](https://mlsanity.com/paper/2106.03252/) (2021)
- [Score and Information for Recursive Exponential Models with Incomplete Data](https://mlsanity.com/paper/1302.1571/) (2013)
- [Bayesian Estimation Under Informative Sampling with Unattenuated Dependence](https://mlsanity.com/paper/1807.05066/) (2018)
- [Bayesian nonparametric mixtures of categorical directed graphs for heterogeneous causal inference](https://mlsanity.com/paper/2409.00453/) (2024)
- [Learning Heterogeneous Ordinal Graphical Models via Bayesian Nonparametric Clustering](https://mlsanity.com/paper/2512.04407/) (2025)
- [Graphical model-based clustering of categorical data](https://mlsanity.com/paper/2601.14849/) (2026)

## Abstract (arXiv)

Public attitudes toward artificial intelligence are heterogeneous, ordinally measured, and poorly captured by any single dependency graph. Existing ordinal structure learners assume a shared directed acyclic graph (DAG) across all respondents; recent heterogeneous ordinal graphical-model approaches focus on subgroup discovery rather than confirmatory cluster-specific DAG estimation; and latent profile analyses discard dependency structure entirely. We introduce a heterogeneous ordinal structure-learning framework combining monotone Gaussian score embedding, Bayesian nonparametric (BNP) complexity discovery via a truncated stick-breaking prior, and confirmatory fixed-K estimation with cluster-specific sparse DAG learning. The key methodological insight is a discovery-to-confirmation workflow: the nonparametric stage calibrates plausible archetype complexity, while inner-validated confirmatory refitting yields stable, interpretable structural estimates. On the 2024 Pew American Trends Panel AI attitudes survey, Wave 152 (W152) survey, (N = 4,788, 8 ordinal items), the confirmatory K*=5 model reduces holdout transformed-score mean squared error (MSE) by 25.8% over a single-graph baseline and by 4.6% over mixture-only clustering. A controlled tiered semi-synthetic benchmark calibrated to W152 structure validates recovery across difficulty regimes and transparently reveals failure modes under stress conditions.