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Marginal Effects for Non-Linear Prediction Functions

Christian A. Scholbeck, Giuseppe Casalicchio, Christoph Molnar, Bernd Bischl, Christian Heumann

arXiv 21 Jan 2022 · Machine Learning · publishedData Mining and Knowledge Discovery (2024) · 8 citations (OpenAlex)

arXiv:2201.08837 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Beta coefficients for linear regression models represent the ideal form of an interpretable feature effect. However, for non-linear models and especially generalized linear models, the estimated coefficients cannot be interpreted as a direct feature effect on the predicted outcome. Hence, marginal effects are typically used as approximations for feature effects, either in the shape of derivatives of the prediction function or forward differences in prediction due to a change in a feature value. While marginal effects are commonly used in many scientific fields, they have not yet been adopted as a model-agnostic interpretation method for machine learning models. This may stem from their inflexibility as a univariate feature effect and their inability to deal with the non-linearities found in black box models. We introduce a new class of marginal effects termed forward marginal effects. We argue to abandon derivatives in favor of better-interpretable forward differences. Furthermore, we generalize marginal effects based on forward differences to multivariate changes in feature values. To account for the non-linearity of prediction functions, we introduce a non-linearity measure for marginal effects. We argue against summarizing feature effects of a non-linear prediction function in a single metric such as the average marginal effect. Instead, we propose to partition the feature space to compute conditional average marginal effects on feature subspaces, which serve as conditional feature effect estimates.

Citation extraction

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Williams R (2012) Using the margins command to estimate and interpret adjusted predictions and marginal effects1.00063100%
2Apley DW, Zhu J (2020) Visualizing the effects of predictor variables in black box supervised learning models0.7373367%
3Bartus T (2005) Estimation of marginal effects using margeff0.73732100%
4Mize TD, Doan L, Long JS (2019) A general framework for comparing predictions and marginal effects across models0.73732100%
5Ribeiro MT, Singh S, Guestrin C (2016) "Why should I trust you?": Explaining the predictions of any classifier0.73732100%
6Hastie T, Tibshirani R, Friedman J (2001) The Elements of Statistical Learning0.6443267%
7Leeper TJ (2018) margins: Marginal effects for model objects0.64422100%
8Slack D, Hilgard S, Jia E, Singh S, Lakkaraju H (2019) Fooling LIME and SHAP: Adversarial attacks on post hoc explanation methods0.64422100%
9Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D,… (2008) Global Sensitivity Analysis: The Primer0.5113233%
10Friedman JH (2001) Greedy function approximation: A gradient boosting machine0.5112250%

Showing the top 10 of 59 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1fmeffects: An R Package for Forward Marginal Effects1.000135