# Neural Network-based Partial-Linear Single-Index Models for Environmental Mixtures Analysis

arXiv: https://arxiv.org/abs/2512.11593 · HTML: https://mlsanity.com/paper/2512.11593/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 61 references that are in the map.
- First posted on arXiv 12 Dec 2025.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Three Factors Influencing Minima in SGD](https://mlsanity.com/paper/1711.04623/) (2017)
- [A quantile-based g-computation approach to addressing the effects of exposure mixtures](https://mlsanity.com/paper/1902.04200/) (2019)
- [Bayesian kernel machine regression-causal mediation analysis](https://mlsanity.com/paper/1811.10453/) (2018)
- [Bayesian Multiple Index Models for Environmental Mixtures](https://mlsanity.com/paper/2101.05352/) (2021)

## Abstract (arXiv)

Evaluating the health effects of complex environmental mixtures remains a central challenge in environmental health research. Existing approaches vary in their flexibility, interpretability, scalability, and support for diverse outcome types, often limiting their utility in real-world applications. To address these limitations, we propose a neural network-based partial-linear single-index (NeuralPLSI) modeling framework that bridges semiparametric regression modeling interpretability with the expressive power of deep learning. The NeuralPLSI model constructs an interpretable exposure index via a learnable projection and models its relationship with the outcome through a flexible neural network. The framework accommodates continuous, binary, and time-to-event outcomes, and supports inference through a bootstrap-based procedure that yields confidence intervals for key model parameters. We evaluated NeuralPLSI through simulation studies under a range of scenarios and applied it to data from the National Health and Nutrition Examination Survey (NHANES) to demonstrate its practical utility. Together, our contributions establish NeuralPLSI as a scalable, interpretable, and versatile modeling tool for mixture analysis. To promote adoption and reproducibility, we release a user-friendly open-source software package that implements the proposed methodology and supports downstream visualization and inference (texttthttps://github.com/hyungrok-do/NeuralPLSI).