Pre Hoc and Co Hoc Explainability: Frameworks for Integrating Interpretability into Machine Learning Training for Enhanced Transparency and Performance
Abstract
1. Introduction
- 1.
- We propose two complementary frameworks for integrating explainability into black-box model training: (i) pre hoc explainability, where a white-box model regularizes the black-box model, and (ii) co hoc explainability, where both models are jointly optimized. These frameworks ensure faithful explanations without post hoc computation overhead and maintain model accuracy.
- 2.
- We extend our frameworks to provide both global and local explanations by incorporating Jensen–Shannon divergence with neighborhood information. Our two-phase approach generates instance-specific explanations that are more stable and faithful than post hoc methods like LIME, while being 30× more computationally efficient at inference time.
- 3.
- We demonstrate through extensive experiments that our frameworks not only improve explainability but also enhance white-box model accuracy by up to 3% through co hoc learning. This finding is particularly valuable for regulated domains like healthcare and finance where interpretable models are mandatory.
2. Related Work
2.1. Explainability Approaches in Machine Learning
2.2. In-Training Explainability Techniques
2.3. Explanation Types and Evaluation
2.4. Factorization Machines
3. Methodology
3.1. Problem Formulation
Enforcing Fidelity
3.2. Pre Hoc Explainability Framework
- 1.
- Train the white-box explainer model on the training data to minimize the binary cross-entropy loss.
- 2.
- Fix the parameters of the explainer model.
- 3.
- Train the black-box predictor model to minimize the combined loss function .
3.3. Co Hoc Explainability Framework
- 1.
- Initialize the parameters of the predictor model and of the explainer model.
- 2.
- For each mini-batch of training data:
- (a)
- Compute the predictions of both models: and .
- (b)
- Calculate the combined loss function .
- (c)
- Update both sets of parameters and using gradient descent.
Comparison of Pre Hoc and Co Hoc Frameworks
3.4. Ensuring Explainer Quality
3.5. Extending to Local Explainability
3.5.1. Local Explainability with Neighborhood Information
3.5.2. Two-Phase Approach for Local Explainability
Algorithm 1 Testing PHASE 2: Computing Local Explanations | |
Require: White-box model , input training instances with their true labels y, nearest neighborhood function , number of neighborhood instances k, testing instance | |
▷ Get k-NN to training instance from training set | |
Compute | ▷ Predictions from explainer model |
for All do | ▷ Get predictor outputs for the local training neighbors |
end for | |
▷ initialize local model to the global model | |
for t = 1 to do | |
for All do | |
▷ Get local explainer outputs for the local training neighbors | |
end for | |
Update Local Explainer Loss using Equation (20) | |
▷ Update using gradient descent | |
end for | |
Extract feature importances feature_importances from using Equation (21) and the set of features in the data | |
return feature_importances |
3.6. Generating Explanations
3.7. Experimental Setup
3.7.1. Datasets
3.7.2. Evaluation Metrics
3.7.3. Implementation Details
4. Results
4.1. Global Explainability Results
4.1.1. Accuracy and Fidelity Trade-Off
4.1.2. Effect of Regularization Parameter
4.2. Local Explainability Results
Comparison with LIME
4.3. Effect of Regularization Parameter on Local Explainability Metrics
4.3.1. Effect of Neighborhood Size
4.3.2. Computational Efficiency
4.4. Qualitative Analysis of Explanations
4.4.1. Global Explanations
4.4.2. Local Explanations
5. Discussion
Limitations and Future Directions
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
AUC | Area Under the ROC Curve |
BB | Black-Box |
BCE | Binary Cross-Entropy |
FM | Factorization Machine |
HELOC | Home Equity Line of Credit |
JS | Jensen–Shannon |
KL | Kullback–Leibler |
LIME | Local Interpretable Model-Agnostic Explanation |
MAD | Mean Absolute Deviation |
ROC | Receiver Operating Characteristic |
SHAP | SHapley Additive exPlanation |
TV | Total Variation |
WB | White-Box |
XAI | eXplainable Artificial Intelligence |
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Model | ML-100k | ML-1M | HELOC | |||
---|---|---|---|---|---|---|
AUC ↑ | Fidelity ↑ | AUC ↑ | Fidelity ↑ | AUC ↑ | Fidelity ↑ | |
Explainer (WB) | 0.7655 ± 0.0042 | - | 0.7882 ± 0.0038 | - | 0.7616 ± 0.0051 | - |
Original (BB) | 0.7784 ± 0.0039 | 0.8287 ± 0.0156 | 0.8078 ± 0.0041 | 0.8875 ± 0.0143 | 0.7703 ± 0.0048 | 0.7728 ± 0.0187 |
Pre hoc (BB) | 0.7801 ± 0.0037 | 0.9094 ± 0.0098 | 0.8033 ± 0.0044 | 0.9404 ± 0.0076 | 0.7698 ± 0.0046 | 0.8454 ± 0.0134 |
Co hoc (BB) | 0.7816 ± 0.0035 | 0.9194 ± 0.0087 | 0.8036 ± 0.0042 | 0.9484 ± 0.0065 | 0.7743 ± 0.0044 | 0.8572 ± 0.0121 |
Explanation Method | Point Fidelity ↑ | Neighborhood Fidelity ↑ | Stability ↓ |
---|---|---|---|
LIME | 0.6083 ± 0.0050 | 0.6600 ± 0.1939 | 0.2152 ± 0.0175 |
Pre hoc Framework | 0.8270 ± 0.0260 | 0.9587 ± 0.0766 | 0.0623 ± 0.0110 |
Co hoc Framework | 0.8300 ± 0.0240 | 0.9647 ± 0.0575 | 0.0502 ± 0.0087 |
Explanation Method | Point Fidelity ↑ | Neighborhood Fidelity ↑ | Stability ↓ |
---|---|---|---|
No-regularization | 0.8183 ± 0.3524 | 0.8050 ± 0.1268 | 0.3524 ± 0.0175 |
Reg | 0.8473 ± 0.0351 | 0.8553 ± 0.1158 | 0.1290 ± 0.0010 |
Reg | 0.8781 ± 0.0195 | 0.8923 ± 0.1043 | 0.1128 ± 0.0009 |
Reg | 0.9370 ± 0.0230 | 0.9353 ± 0.0737 | 0.0815 ± 0.0019 |
Reg | 0.9740 ± 0.0237 | 0.9903 ± 0.0329 | 0.0189 ± 0.0041 |
Reg | 0.9824 ± 0.0234 | 0.9953 ± 0.0215 | 0.0078 ± 0.0010 |
Reg | 0.9951 ± 0.0117 | 0.9953 ± 0.0215 | 0.0078 ± 0.0010 |
Neighborhood Size | Neighborhood Fidelity ↑ | Stability ↓ | Computation Time (s) |
---|---|---|---|
0.8833 ± 0.1939 | 0.2152 ± 0.0175 | 0.0121 ± 0.0014 | |
0.9350 ± 0.0381 | 0.0505 ± 0.0098 | 0.0127 ± 0.0009 | |
0.9670 ± 0.0013 | 0.0015 ± 0.00006 | 0.0144 ± 0.0061 |
Method | Additional Training Time (s) | Avg Explanation Time (s) | Total Time for Single Instance (s) | Total Time for 100 Instances (s) |
---|---|---|---|---|
LIME | - | 0.3812 ± 0.0828 | 0.3812 ± 0.0828 | 62.580 |
Pre hoc | 5.1020 ± 0.0315 | 0.0110 ± 0.0015 | 5.1130 ± 0.0330 | 6.202 |
Co hoc | 5.3960 ± 0.0330 | 0.0135 ± 0.0030 | 5.4095 ± 0.0360 | 6.746 |
Method | Additional Training Time (s) | Avg Explanation Time (s) | Total Time for Single Instance (s) | Total Time for 100 Instances (s) |
---|---|---|---|---|
LIME | - | 0.4523 ± 0.0912 | 0.4523 ± 0.0912 | 45.23 |
Pre hoc | 8.989 ± 0.595 | 0.0186 ± 0.0013 | 9.0076 ± 0.5963 | 10.849 |
Co hoc | 9.383 ± 0.623 | 0.0211 ± 0.0028 | 9.4041 ± 0.6258 | 11.493 |
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Acun, C.; Nasraoui, O. Pre Hoc and Co Hoc Explainability: Frameworks for Integrating Interpretability into Machine Learning Training for Enhanced Transparency and Performance. Appl. Sci. 2025, 15, 7544. https://doi.org/10.3390/app15137544
Acun C, Nasraoui O. Pre Hoc and Co Hoc Explainability: Frameworks for Integrating Interpretability into Machine Learning Training for Enhanced Transparency and Performance. Applied Sciences. 2025; 15(13):7544. https://doi.org/10.3390/app15137544
Chicago/Turabian StyleAcun, Cagla, and Olfa Nasraoui. 2025. "Pre Hoc and Co Hoc Explainability: Frameworks for Integrating Interpretability into Machine Learning Training for Enhanced Transparency and Performance" Applied Sciences 15, no. 13: 7544. https://doi.org/10.3390/app15137544
APA StyleAcun, C., & Nasraoui, O. (2025). Pre Hoc and Co Hoc Explainability: Frameworks for Integrating Interpretability into Machine Learning Training for Enhanced Transparency and Performance. Applied Sciences, 15(13), 7544. https://doi.org/10.3390/app15137544