# Conditional Rank-Rank Regression via Deep Conditional Transformation Models

arXiv: https://arxiv.org/abs/2603.07230 · HTML: https://mlsanity.com/paper/2603.07230/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 52 references that are in the map.
- First posted on arXiv 7 Mar 2026.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Conditional Transformation Models](https://mlsanity.com/paper/2010.07860/) (2020)
- [Most Likely Transformations](https://mlsanity.com/paper/1508.06749/) (2015)
- [Deep transformation models: Tackling complex regression problems with neural network based transformation models](https://mlsanity.com/paper/2004.00464/) (2020)
- [Deep interpretable ensembles](https://mlsanity.com/paper/2205.12729/) (2022)
- [Conditional Rank-Rank Regression](https://mlsanity.com/paper/2407.06387/) (2024)

## Abstract (arXiv)

Intergenerational mobility quantifies the transmission of socio-economic outcomes from parents to children. While rank-rank regression (RRR) is standard, adding covariates directly (RRRX) often yields parameters with unclear interpretation. Conditional rank-rank regression (CRRR) resolves this by using covariate-adjusted (conditional) ranks to measure within-group mobility. We improve and extend CRRR by estimating conditional ranks with a deep conditional transformation model (DCTM) and cross-fitting, enabling end-to-end conditional distribution learning with structural constraints and strong performance under nonlinearity, high-order interactions, and discrete ordered outcomes where the distributional regression used in traditional CRRR may be cumbersome or prone to misconfiguration. We further extend CRRR to discrete outcomes via an ω-indexed conditional-rank definition and study sensitivity to ω. For continuous outcomes, we establish an asymptotic theory for the proposed estimators and verify the validity of exchangeable bootstrap inference. Simulations across simple/complex continuous and discrete ordered designs show clear accuracy gains in challenging settings. Finally, we apply our method to two empirical studies, revealing substantial within-group persistence in U.S. income and pronounced gender differences in educational mobility in India.