mlsanityData to 7 Oct 2026

Relating the Partial Dependence Plot and Permutation Feature Importance to the Data Generating Process

arXiv 2109.01433 ↗First posted 3 Sep 2021stat.ML cs.LGcited by 24

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Abstract (arXiv)

Scientists and practitioners increasingly rely on machine learning to model data and draw conclusions. Compared to statistical modeling approaches, machine learning makes fewer explicit assumptions about data structures, such as linearity. However, their model parameters usually cannot be easily related to the data generating process. To learn about the modeled relationships, partial dependence (PD) plots and permutation feature importance (PFI) are often used as interpretation methods. However, PD and PFI lack a theory that relates them to the data generating process. We formalize PD and PFI as statistical estimators of ground truth estimands rooted in the data generating process. We show that PD and PFI estimates deviate from this ground truth due to statistical biases, model variance and Monte Carlo approximation errors. To account for model variance in PD and PFI estimation, we propose the learner-PD and the learner-PFI based on model refits, and propose corrected variance and confidence interval estimators.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 10 of its 42 references that are in the map. First posted on arXiv 3 Sep 2021.

Builds on

10 of 42 references.

References · 10

  1. 2018All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneouslycited by 364
  2. 2016Model-Agnostic Interpretability of Machine Learningcited by 219
  3. 2016Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Modelscited by 212
  4. 2021Accounting for Variance in Machine Learning Benchmarkscited by 195
  5. 2021Cross-validation: what does it estimate and how well does it do it?cited by 65
  6. 2020Model-agnostic Feature Importance and Effects with Dependent Features -- A Conditional Subgroup Approachcited by 37
  7. 2019Testing Conditional Independence in Supervised Learning Algorithmscited by 27
  8. 2020Floodgate: inference for model-free variable importancecited by 15
  9. 2019Sampling, Intervention, Prediction, Aggregation: A Generalized Framework for Model-Agnostic Interpretationscited by 9
  10. 2020Nonparametric Feature Impact and Importancecited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 6; 2024: 8; 2025: 4; 2026: 4.

24 papers.

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  1. 2023Dear XAI Community, We Need to Talk! Fundamental Misconceptions in Current XAI Researchcited by 22
  2. 2022Scientific Inference With Interpretable Machine Learning: Analyzing Models to Learn About Real-World Phenomenacited by 21
  3. 2024A Guide to Feature Importance Methods for Scientific Inferencecited by 11
  4. 2023Performance is not enough: the story told by a Rashomon quartetcited by 9
  5. 2023RHALE: Robust and Heterogeneity-aware Accumulated Local Effectscited by 8
  6. 2022Ultra-marginal Feature Importance: Learning from Data with Causal Guaranteescited by 6
  7. 2023Confident Feature Rankingcited by 6
  8. 2025A Statistical Case Against Empirical Human-AI Alignmentcited by 6
  9. 2024Why You Should Not Trust Interpretations in Machine Learning: Adversarial Attacks on Partial Dependence Plotscited by 5
  10. 2024Interpretable Machine Learning for Survival Analysiscited by 4
  11. 2024Fast Estimation of Partial Dependence Functions using Treescited by 4
  12. 2023Explaining and visualizing black-box models through counterfactual pathscited by 2
12 more
  1. 2024On the Robustness of Global Feature Effect Explanationscited by 2
  2. 2026Analyzing Error Sources in Global Feature Effect Estimationcited by 1
  3. 2026xplainfi: Feature Importance and Statistical Inference for Machine Learning in Rcited by 1
  4. 2026MinShap: A Shapley-Based Framework for Feature Redundancycited by 1
  5. 2023Innovations in Agricultural Forecasting: A Multivariate Regression Study on Global Crop Yield Predictioncited by 0
  6. 2024mlr3summary: Concise and interpretable summaries for machine learning modelscited by 0
  7. 2024Statistics and explainability: a fruitful alliancecited by 0
  8. 2024Targeted Learning for Variable Importancecited by 0
  9. 2025Comparing Model-agnostic Feature Selection Methods through Relative Efficiencycited by 0
  10. 2025Interval Prediction of Annual Average Daily Traffic on Local Roads via Quantile Random Forest with High-Dimensional Spatial Datacited by 0
  11. 2025Imputation Uncertainty in Interpretable Machine Learning Methodscited by 0
  12. 2026A Resilience-as-a-Service assessment framework for coordinated disruption response in interdependent urban transit systemscited by 0