# A Monotone Single-Index Modal Regression Powered by Deep Neural Networks for Non-Gaussian Periodontal Data

arXiv: https://arxiv.org/abs/2505.02153 · HTML: https://mlsanity.com/paper/2505.02153/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 53 references that are in the map.
- First posted on arXiv 4 May 2025.

## Builds on (most cited first, 11 of 11)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Neural Networks Efficiently Learn Low-Dimensional Representations with SGD](https://mlsanity.com/paper/2209.14863/) (2022)
- [Constrained Monotonic Neural Networks](https://mlsanity.com/paper/2205.11775/) (2022)
- [Nonparametric modal regression](https://mlsanity.com/paper/1412.1716/) (2014)
- [A Statistical Learning Approach to Modal Regression](https://mlsanity.com/paper/1702.05960/) (2017)
- [Modal Regression using Kernel Density Estimation: a Review](https://mlsanity.com/paper/1710.07004/) (2017)
- [Generative Quantile Regression with Variability Penalty](https://mlsanity.com/paper/2301.03661/) (2023)
- [Generative Multiple-purpose Sampler for Weighted M-estimation](https://mlsanity.com/paper/2006.00767/) (2020)
- [Bayesian modelling of skewness and kurtosis with two-piece scale and shape distributions](https://mlsanity.com/paper/1406.7674/) (2014)
- [Scale mixture of skew-normal linear mixed models with within-subject serial dependence](https://mlsanity.com/paper/2002.01040/) (2020)
- [Bayesian Modal Regression based on Mixture Distributions](https://mlsanity.com/paper/2211.10776/) (2022)

## Abstract (arXiv)

Pocket depth (PD) is a widely used biomarker for diagnosing risk of periodontal disease (PrD). However, PD typically exhibits skewness and heavy-tailedness, and its relationship with clinical risk factors is often nonlinear. Motivated by PrD studies, this paper develops a robust single-index modal regression framework for analyzing skewed and heavy-tailed data. Our method has the following novel features: (a) a flexible two-piece scale Student-t error distribution that generalizes both normal and two-piece scale normal distributions; (b) a neural network with guaranteed monotonicity constraints to estimate the unknown single-index function; and (c) theoretical revonesupport, including model identifiability and a universal approximation theorem. Our single-index model combines the flexibility of neural networks and the two-piece scaled Student-t distribution, delivering robust mode-based estimation that is resistant to outliers, while retaining clinical interpretability through parametric index coefficients. We demonstrate the performance of our method through simulation studies, and an application to PrD electronic health records obtained from the HealthPartners Institute of Minnesota. The proposed methodology is implemented in the textttR package hrefhttps://doi.org/10.32614/CRAN.package.DNNSIMtextttDNNSIM.