# Preferential Mixture-of-Experts: Interpretable Models that Rely on Human Expertise as much as Possible

arXiv: https://arxiv.org/abs/2101.05360 · HTML: https://mlsanity.com/paper/2101.05360/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- Builds on 12 of its 37 references that are in the map.
- First posted on arXiv 13 Jan 2021.

## Placed in

- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Builds on (most cited first, 12 of 12)

- [Consistent Estimators for Learning to Defer to an Expert](https://mlsanity.com/paper/2006.01862/) (2020)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Learning to Complement Humans](https://mlsanity.com/paper/2005.00582/) (2020)
- [The Algorithmic Automation Problem: Prediction, Triage, and Human Effort](https://mlsanity.com/paper/1903.12220/) (2019)
- [Expert-Augmented Machine Learning](https://mlsanity.com/paper/1903.09731/) (2019)
- [Parallel and Distributed Methods for Nonconvex Optimization--Part II: Applications](https://mlsanity.com/paper/1601.04059/) (2016)
- [Learning Credible Models](https://mlsanity.com/paper/1711.03190/) (2017)
- [Gradient descent with nonconvex constraints: local concavity determines convergence](https://mlsanity.com/paper/1703.07755/) (2017)
- [Knowledge Enhanced Hybrid Neural Network for Text Matching](https://mlsanity.com/paper/1611.04684/) (2016)
- [Machine Learning with Abstention for Automated Liver Disease Diagnosis](https://mlsanity.com/paper/1811.04463/) (2018)
- [KINN: Incorporating Expert Knowledge in Neural Networks](https://mlsanity.com/paper/1902.05653/) (2019)

## Built on by (most cited first, 19 of 19)

- [Who Should Predict? Exact Algorithms For Learning to Defer to Humans](https://mlsanity.com/paper/2301.06197/) (2023)
- [Learning to Defer to Multiple Experts: Consistent Surrogate Losses, Confidence Calibration, and Conformal Ensembles](https://mlsanity.com/paper/2210.16955/) (2022)
- [Sample Efficient Learning of Predictors that Complement Humans](https://mlsanity.com/paper/2207.09584/) (2022)
- [Principled Approaches for Learning to Defer with Multiple Experts](https://mlsanity.com/paper/2310.14774/) (2023)
- [Learning to Defer to a Population: A Meta-Learning Approach](https://mlsanity.com/paper/2403.02683/) (2024)
- [Realizable H-Consistent and Bayes-Consistent Loss Functions for Learning to Defer](https://mlsanity.com/paper/2407.13732/) (2024)
- [Interpretable Mixture of Experts](https://mlsanity.com/paper/2206.02107/) (2022)
- [Mastering Multiple-Expert Routing: Realizable H-Consistency and Strong Guarantees for Learning to Defer](https://mlsanity.com/paper/2506.20650/) (2025)
- [Budgeted Multiple-Expert Deferral](https://mlsanity.com/paper/2510.26706/) (2025)
- [Learning-to-defer for sequential medical decision-making under uncertainty](https://mlsanity.com/paper/2109.06312/) (2021)
- [AI, Meet Human: Learning Paradigms for Hybrid Decision Making Systems](https://mlsanity.com/paper/2402.06287/) (2024)
- [Learning to Complement and to Defer to Multiple Users](https://mlsanity.com/paper/2407.07003/) (2024)
- [How Can We Diagnose and Treat Bias in Large Language Models for Clinical Decision-Making?](https://mlsanity.com/paper/2410.16574/) (2024)
- [Mixture of Concept Bottleneck Experts](https://mlsanity.com/paper/2602.02886/) (2026)
- [Optimized Deferral for Imbalanced Settings](https://mlsanity.com/paper/2604.27723/) (2026)
- [Human-AI Collaborative Multi-modal Multi-rater Learning for Endometriosis Diagnosis](https://mlsanity.com/paper/2409.02046/) (2024)
- [MoRE-LLM: Mixture of Rule Experts Guided by a Large Language Model](https://mlsanity.com/paper/2503.22731/) (2025)
- [Calibrating conditional risk](https://mlsanity.com/paper/2604.20409/) (2026)
- [Towards Integrating Personal Knowledge into Test-Time Predictions](https://mlsanity.com/paper/2406.08636/) (2024)

## Abstract (arXiv)

We propose Preferential MoE, a novel human-ML mixture-of-experts model that augments human expertise in decision making with a data-based classifier only when necessary for predictive performance. Our model exhibits an interpretable gating function that provides information on when human rules should be followed or avoided. The gating function is maximized for using human-based rules, and classification errors are minimized. We propose solving a coupled multi-objective problem with convex subproblems. We develop approximate algorithms and study their performance and convergence. Finally, we demonstrate the utility of Preferential MoE on two clinical applications for the treatment of Human Immunodeficiency Virus (HIV) and management of Major Depressive Disorder (MDD).