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When fitting black box supervised learning models (e.g., complex trees, neural networks, boosted trees, random forests, nearest neighbors, local kernel-weighted methods, etc.), visualizing the main effects of the individual predictor…

Methodology · Statistics 2019-08-21 Daniel W. Apley , Jingyu Zhu

Variable importance measures (VIMs) aim to quantify the contribution of each input covariate to the predictability of a given output. With the growing interest in explainable AI, numerous VIMs have been proposed, many of which are heuristic…

Methodology · Statistics 2025-09-23 Angel Reyero-Lobo , Pierre Neuvial , Bertrand Thirion

Global variable importance measures are commonly used to interpret the results of machine learning models. Local variable importance techniques assess how variables contribute to individual observations. Current, popular methods, including…

Machine Learning · Statistics 2026-03-12 Kelvyn K. Bladen , Adele Cutler , D. Richard Cutler , Kevin R. Moon

One of the key elements of explanatory analysis of a predictive model is to assess the importance of individual variables. Rapid development of the area of predictive model exploration (also called explainable artificial intelligence or…

Machine Learning · Computer Science 2021-04-09 Katarzyna Pekala , Katarzyna Woznica , Przemyslaw Biecek

Interpreting black-box machine learning models is challenging due to their strong dependence on data and inherently non-parametric nature. This paper reintroduces the concept of importance through "Marginal Variable Importance Metric"…

Machine Learning · Statistics 2025-01-30 Mohammad Kaviul Anam Khan , Olli Saarela , Rafal Kustra

This paper reviews and advocates against the use of permute-and-predict (PaP) methods for interpreting black box functions. Methods such as the variable importance measures proposed for random forests, partial dependence plots, and…

Methodology · Statistics 2021-10-11 Giles Hooker , Lucas Mentch , Siyu Zhou

We introduce a variable importance measure to quantify the impact of individual input variables to a black box function. Our measure is based on the Shapley value from cooperative game theory. Many measures of variable importance operate by…

Machine Learning · Computer Science 2020-10-05 Masayoshi Mase , Art B. Owen , Benjamin Seiler

Motivated by applications in precision medicine and treatment effect heterogeneity, recent research has focused on estimating conditional average treatment effects (CATEs) using machine learning (ML). CATE estimates may represent…

Methodology · Statistics 2025-12-30 Oliver J. Hines , Karla Diaz-Ordaz , Stijn Vansteelandt

Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular,…

Statistics Theory · Mathematics 2022-10-25 Julien Demange-Chryst , François Bachoc , Jérôme Morio

Accumulated Local Effect (ALE) is a method for accurately estimating feature effects, overcoming fundamental failure modes of previously-existed methods, such as Partial Dependence Plots. However, ALE's approximation, i.e. the method for…

Machine Learning · Computer Science 2022-10-11 Vasilis Gkolemis , Theodore Dalamagas , Christos Diou

Variable importance plays a pivotal role in interpretable machine learning as it helps measure the impact of factors on the output of the prediction model. Model agnostic methods based on the generation of "null" features via permutation…

We analyze two widely used local attribution methods, Local Shapley Values and LIME, which aim to quantify the contribution of a feature value $x_i$ to a specific prediction $f(x_1, \dots, x_p)$. Despite their widespread use, we identify…

Machine Learning · Statistics 2026-04-14 Salim I. Amoukou , Nicolas J-B. Brunel

We develop a new, principled algorithm for estimating the contribution of training data points to the behavior of a deep learning model, such as a specific prediction it makes. Our algorithm estimates the AME, a quantity that measures the…

Machine Learning · Computer Science 2022-06-22 Jinkun Lin , Anqi Zhang , Mathias Lecuyer , Jinyang Li , Aurojit Panda , Siddhartha Sen

Accumulated Local Effects (ALE) is a model-agnostic approach for global explanations of the results of black-box machine learning (ML) algorithms. There are at least three challenges with conducting statistical inference based on ALE:…

Machine Learning · Computer Science 2024-02-14 Chitu Okoli

Current practice in interpretable machine learning often focuses on explaining the final model trained from data, e.g., by using the Shapley additive explanations (SHAP) method. The recently developed Shapley variable importance cloud…

Machine Learning · Computer Science 2022-12-19 Yilin Ning , Mingxuan Liu , Nan Liu

Variable importance is defined as a measure of each regressor's contribution to model fit. Using R^2 as the fit criterion in linear models leads to the Shapley value (LMG) and proportionate value (PMVD) as variable importance measures.…

Methodology · Statistics 2022-12-08 Charles D. Coleman

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

Methodology · Statistics 2026-03-03 Linglingzhi Zhu , Jonghyeok Lee , Yao Xie

Variational auto-encoders (VAE) are popular deep latent variable models which are trained by maximizing an Evidence Lower Bound (ELBO). To obtain tighter ELBO and hence better variational approximations, it has been proposed to use…

Machine Learning · Statistics 2021-07-22 Achille Thin , Nikita Kotelevskii , Arnaud Doucet , Alain Durmus , Eric Moulines , Maxim Panov

In recent years, a large amount of model-agnostic methods to improve the transparency, trustability and interpretability of machine learning models have been developed. We introduce local feature importance as a local version of a recent…

Machine Learning · Statistics 2020-07-15 Giuseppe Casalicchio , Christoph Molnar , Bernd Bischl

The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model. In this work, we suggest new estimators of these sensitivity indices. When the input distribution is…

Statistics Theory · Mathematics 2020-02-14 Baptiste Broto , François Bachoc , Marine Depecker
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