# Incorporating Interpretable Output Constraints in Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2010.10969 · HTML: https://mlsanity.com/paper/2010.10969/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2020.

## Built on by (most cited first, 10 of 10)

- [A Critical Survey on Fairness Benefits of Explainable AI](https://mlsanity.com/paper/2310.13007/) (2023)
- [Deep Learning for Bayesian Optimization of Scientific Problems with High-Dimensional Structure](https://mlsanity.com/paper/2104.11667/) (2021)
- [Model Selection for Bayesian Autoencoders](https://mlsanity.com/paper/2106.06245/) (2021)
- [Toward Operationalizing Pipeline-aware ML Fairness: A Research Agenda for Developing Practical Guidelines and Tools](https://mlsanity.com/paper/2309.17337/) (2023)
- [Posterior Regularized Bayesian Neural Network Incorporating Soft and Hard Knowledge Constraints](https://mlsanity.com/paper/2210.08608/) (2022)
- [Regularized KL-Divergence for Well-Defined Function-Space Variational Inference in Bayesian neural networks](https://mlsanity.com/paper/2406.04317/) (2024)
- [Bayesian Entropy Neural Networks for Physics-Aware Prediction](https://mlsanity.com/paper/2407.01015/) (2024)
- [Optimization Proxies using Limited Labeled Data and Training Time -- A Semi-Supervised Bayesian Neural Network Approach](https://mlsanity.com/paper/2410.03085/) (2024)
- [Augmenting Neural Networks with Priors on Function Values](https://mlsanity.com/paper/2202.04798/) (2022)
- [Incorporating functional summary information in Bayesian neural networks using a Dirichlet process likelihood approach](https://mlsanity.com/paper/2207.01234/) (2022)

## Abstract (arXiv)

Domains where supervised models are deployed often come with task-specific constraints, such as prior expert knowledge on the ground-truth function, or desiderata like safety and fairness. We introduce a novel probabilistic framework for reasoning with such constraints and formulate a prior that enables us to effectively incorporate them into Bayesian neural networks (BNNs), including a variant that can be amortized over tasks. The resulting Output-Constrained BNN (OC-BNN) is fully consistent with the Bayesian framework for uncertainty quantification and is amenable to black-box inference. Unlike typical BNN inference in uninterpretable parameter space, OC-BNNs widen the range of functional knowledge that can be incorporated, especially for model users without expertise in machine learning. We demonstrate the efficacy of OC-BNNs on real-world datasets, spanning multiple domains such as healthcare, criminal justice, and credit scoring.