Learning outside the Black-Box: The pursuit of interpretable models
Not on the map. Why?
Abstract (arXiv)
Machine Learning has proved its ability to produce accurate models but the deployment of these models outside the machine learning community has been hindered by the difficulties of interpreting these models. This paper proposes an algorithm that produces a continuous global interpretation of any given continuous black-box function. Our algorithm employs a variation of projection pursuit in which the ridge functions are chosen to be Meijer G-functions, rather than the usual polynomial splines. Because Meijer G-functions are differentiable in their parameters, we can tune the parameters of the representation by gradient descent; as a consequence, our algorithm is efficient. Using five familiar data sets from the UCI repository and two familiar machine learning algorithms, we demonstrate that our algorithm produces global interpretations that are both highly accurate and parsimonious (involve a small number of terms). Our interpretations permit easy understanding of the relative importance of features and feature interactions. Our interpretation algorithm represents a leap forward from the previous state of the art.
Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Nov 2020.
Builds on
No reference list yet.
Built on by
Citing papers per year: 2021: 2; 2022: 5; 2023: 5; 2024: 4; 2025: 1.
17 papers.
Sort:
- 2022From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AIcited by 299
- 2021On the Computational Intelligibility of Boolean Classifierscited by 40
- 2021Precise characterization of the prior predictive distribution of deep ReLU networkscited by 28
- 2023Deep Generative Symbolic Regressioncited by 27
- 2022Label-Free Explainability for Unsupervised Modelscited by 14
- 2023On (assessing) the fairness of risk score modelscited by 12
- 2024ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inferencecited by 12
- 2022AutoPrognosis 2.0: Democratizing Diagnostic and Prognostic Modeling in Healthcare with Automated Machine Learningcited by 10
- 2022Symbolic Recovery of Differential Equations: The Identifiability Problemcited by 8
- 2022D-CIPHER: Discovery of Closed-form Partial Differential Equationscited by 7
- 2024Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradientscited by 3
- 2023Symbolic Metamodels for Interpreting Black-boxes Using Primitive Functionscited by 2
5 more
- 2023How Well Do Feature-Additive Explainers Explain Feature-Additive Predictors?cited by 2
- 2024AdaptGrad: Adaptive Sampling to Reduce Noisecited by 2
- 2023Interpreting deep embeddings for disease progression clusteringcited by 1
- 2024Axiomatization of Gradient Smoothing in Neural Networkscited by 0
- 2025ITL-LIME: Instance-Based Transfer Learning for Enhancing Local Explanations in Low-Resource Data Settingscited by 0
- 2025ITL-LIME: Instance-Based Transfer Learning for Enhancing Local Explanations in Low-Resource Data Settings19 Aug 2025
- 2024AdaptGrad: Adaptive Sampling to Reduce Noise10 Oct 2024
- 2024Axiomatization of Gradient Smoothing in Neural Networks29 Jun 2024
- 2024ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inference16 Mar 2024
- 2024Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradients10 Jan 2024
- 2023Deep Generative Symbolic Regression30 Dec 2023
- 2023How Well Do Feature-Additive Explainers Explain Feature-Additive Predictors?27 Oct 2023
- 2023Interpreting deep embeddings for disease progression clustering12 Jul 2023
- 2023On (assessing) the fairness of risk score models17 Feb 2023
- 2023Symbolic Metamodels for Interpreting Black-boxes Using Primitive Functions9 Feb 2023
- 2022AutoPrognosis 2.0: Democratizing Diagnostic and Prognostic Modeling in Healthcare with Automated Machine Learning21 Oct 2022
- 2022Symbolic Recovery of Differential Equations: The Identifiability Problem15 Oct 2022
5 more
- 2022D-CIPHER: Discovery of Closed-form Partial Differential Equations21 Jun 2022
- 2022Label-Free Explainability for Unsupervised Models3 Mar 2022
- 2022From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AI20 Jan 2022
- 2021Precise characterization of the prior predictive distribution of deep ReLU networks11 Jun 2021
- 2021On the Computational Intelligibility of Boolean Classifiers13 Apr 2021
- 2022From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AIcited by 299
- 2021On the Computational Intelligibility of Boolean Classifierscited by 40
- 2021Precise characterization of the prior predictive distribution of deep ReLU networkscited by 28
- 2023Deep Generative Symbolic Regressioncited by 27
- 2022Label-Free Explainability for Unsupervised Modelscited by 14
- 2023On (assessing) the fairness of risk score modelscited by 12
- 2024ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inferencecited by 12
- 2022AutoPrognosis 2.0: Democratizing Diagnostic and Prognostic Modeling in Healthcare with Automated Machine Learningcited by 10
- 2022Symbolic Recovery of Differential Equations: The Identifiability Problemcited by 8
- 2022D-CIPHER: Discovery of Closed-form Partial Differential Equationscited by 7
- 2024Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradientscited by 3
- 2023Symbolic Metamodels for Interpreting Black-boxes Using Primitive Functionscited by 2
12 most cited of 17 All 17 (JSON)
- 2025ITL-LIME: Instance-Based Transfer Learning for Enhancing Local Explanations in Low-Resource Data Settings19 Aug 2025
- 2024AdaptGrad: Adaptive Sampling to Reduce Noise10 Oct 2024
- 2024Axiomatization of Gradient Smoothing in Neural Networks29 Jun 2024
- 2024ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inference16 Mar 2024
- 2024Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradients10 Jan 2024
- 2023Deep Generative Symbolic Regression30 Dec 2023
- 2023How Well Do Feature-Additive Explainers Explain Feature-Additive Predictors?27 Oct 2023
- 2023Interpreting deep embeddings for disease progression clustering12 Jul 2023
- 2023On (assessing) the fairness of risk score models17 Feb 2023
- 2023Symbolic Metamodels for Interpreting Black-boxes Using Primitive Functions9 Feb 2023
- 2022AutoPrognosis 2.0: Democratizing Diagnostic and Prognostic Modeling in Healthcare with Automated Machine Learning21 Oct 2022
- 2022Symbolic Recovery of Differential Equations: The Identifiability Problem15 Oct 2022
12 newest of 17 All 17 (JSON)