# Matching Learned Causal Effects of Neural Networks with Domain Priors

arXiv: https://arxiv.org/abs/2111.12490 · HTML: https://mlsanity.com/paper/2111.12490/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 62 references that are in the map.
- First posted on arXiv 24 Nov 2021.

## Builds on (most cited first, 30 of 30)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [Right for the Right Reasons: Training Differentiable Models by Constraining their Explanations](https://mlsanity.com/paper/1703.03717/) (2017)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Counterfactual Data Augmentation for Mitigating Gender Stereotypes in Languages with Rich Morphology](https://mlsanity.com/paper/1906.04571/) (2019)
- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/1906.04477/) (2019)
- [Interpretations are useful: penalizing explanations to align neural networks with prior knowledge](https://mlsanity.com/paper/1909.13584/) (2019)
- [Explaining Classifiers with Causal Concept Effect (CaCE)](https://mlsanity.com/paper/1907.07165/) (2019)
- [Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness](https://mlsanity.com/paper/1811.00007/) (2018)
- [Counterfactual Data Augmentation using Locally Factored Dynamics](https://mlsanity.com/paper/2007.02863/) (2020)
- [Learning Counterfactual Representations for Estimating Individual Dose-Response Curves](https://mlsanity.com/paper/1902.00981/) (2019)
- [Neural Network Attributions: A Causal Perspective](https://mlsanity.com/paper/1902.02302/) (2019)
- [Knowledge Transfer with Jacobian Matching](https://mlsanity.com/paper/1803.00443/) (2018)
- [Deep Lattice Networks and Partial Monotonic Functions](https://mlsanity.com/paper/1709.06680/) (2017)
- [A causal framework for explaining the predictions of black-box sequence-to-sequence models](https://mlsanity.com/paper/1707.01943/) (2017)
- [Evaluating and Mitigating Bias in Image Classifiers: A Causal Perspective Using Counterfactuals](https://mlsanity.com/paper/2009.08270/) (2020)
- [CausalVAE: Structured Causal Disentanglement in Variational Autoencoder](https://mlsanity.com/paper/2004.08697/) (2020)
- [CASTLE: Regularization via Auxiliary Causal Graph Discovery](https://mlsanity.com/paper/2009.13180/) (2020)
- [Monotonic Calibrated Interpolated Look-Up Tables](https://mlsanity.com/paper/1505.06378/) (2015)
- [Counterexample-Guided Learning of Monotonic Neural Networks](https://mlsanity.com/paper/2006.08852/) (2020)
- [Causal Regularization](https://mlsanity.com/paper/1906.12179/) (2019)
- [How to Incorporate Monotonicity in Deep Networks While Preserving Flexibility?](https://mlsanity.com/paper/1909.10662/) (2019)
- [Contrastive ACE: Domain Generalization Through Alignment of Causal Mechanisms](https://mlsanity.com/paper/2106.00925/) (2021)
- [A Causal Lens for Peeking into Black Box Predictive Models: Predictive Model Interpretation via Causal Attribution](https://mlsanity.com/paper/2008.00357/) (2020)
- [Supervising Feature Influence](https://mlsanity.com/paper/1803.10815/) (2018)

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

- [Probing Classifiers are Unreliable for Concept Removal and Detection](https://mlsanity.com/paper/2207.04153/) (2022)
- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Knowledge-augmented Deep Learning and Its Applications: A Survey](https://mlsanity.com/paper/2212.00017/) (2022)
- [Toward Operationalizing Pipeline-aware ML Fairness: A Research Agenda for Developing Practical Guidelines and Tools](https://mlsanity.com/paper/2309.17337/) (2023)
- [Towards Learning and Explaining Indirect Causal Effects in Neural Networks](https://mlsanity.com/paper/2303.13850/) (2023)
- [Navigating causal deep learning](https://mlsanity.com/paper/2212.00911/) (2022)
- [Enhancing the Performance of Neural Networks Through Causal Discovery and Integration of Domain Knowledge](https://mlsanity.com/paper/2311.17303/) (2023)
- [On Measuring Intrinsic Causal Attributions in Deep Neural Networks](https://mlsanity.com/paper/2505.09660/) (2025)
- [Tuning Derivatives for Causal Fairness in Machine Learning](https://mlsanity.com/paper/2605.05882/) (2026)
- [XAI-Refine: An Automated Explanation-Knowledge Loop for Brain-Age Prediction](https://mlsanity.com/paper/2609.09388/) (2026)

## Abstract (arXiv)

A trained neural network can be interpreted as a structural causal model (SCM) that provides the effect of changing input variables on the model's output. However, if training data contains both causal and correlational relationships, a model that optimizes prediction accuracy may not necessarily learn the true causal relationships between input and output variables. On the other hand, expert users often have prior knowledge of the causal relationship between certain input variables and output from domain knowledge. Therefore, we propose a regularization method that aligns the learned causal effects of a neural network with domain priors, including both direct and total causal effects. We show that this approach can generalize to different kinds of domain priors, including monotonicity of causal effect of an input variable on output or zero causal effect of a variable on output for purposes of fairness. Our experiments on twelve benchmark datasets show its utility in regularizing a neural network model to maintain desired causal effects, without compromising on accuracy. Importantly, we also show that a model thus trained is robust and gets improved accuracy on noisy inputs.