Hooker Mentch Zhou 2021 - References and Acknowledgments

Summary

This note covers the back matter of Hooker, Mentch & Zhou (2021): author affiliations, funding acknowledgments, and the 46-entry reference list (pp. 18-21). The references are grouped by role in the argument, with full venue, the section(s) where each is cited, and the vault note that discusses it. In the body notes these works are cited inline, often without a venue, and this note is where those venues are recorded. Use it to trace a claim back to its primary source, or to see which literatures the paper draws on: random-forest importance bias, conditional and knockoff methods, re-learning tests, functional ANOVA and Sobol indices, and local explanations.

Overview

Authors and affiliations (p. 1 footnotes): Giles Hooker, University of California, Berkeley; Lucas Mentch, University of Pittsburgh; Siyu Zhou, University of Pittsburgh.

Acknowledgments (p. 18)

The work was “partially supported by NSF grants DMS-1712554, DMS-1712041 and DMS-2015400 as well as the Center for Research Computing at the University of Pittsburgh.”

The reference list has 46 entries. Four involve the first author on functional ANOVA and additive-model explanation (Hooker 2007; Lou et al. 2013; Tan et al. 2018a, b). Five are the authors’ own earlier work on tree importance and random-forest inference (Zhou & Hooker 2019; Mentch & Hooker 2016, 2017; Coleman, Peng & Mentch 2019; Mentch & Zhou 2020). The paper builds on this earlier work for both the explanation and the remedies.

Main Content

1. Permute-and-predict tools and their origins

Reference	Venue	Cited in	Role	Vault note
Breiman, L. (2001). Random Forests	Machine Learning 45, 5-32	§1	Origin of permutation (OOB) variable importance	Permute-and-Predict Extrapolation in Variable Importance
Friedman, J. H. (2001). Greedy function approximation: a gradient boosting machine	Annals of Statistics, 1189-1232	§1	Origin of partial dependence plots; split-improvement importance	Permute-and-Predict Extrapolation in Variable Importance
Goldstein, A., Kapelner, A., Bleich, J. & Pitkin, E. (2015). Peeking inside the black box: visualizing statistical learning with plots of individual conditional expectation	J. Computational and Graphical Statistics 24(1), 44-65	§1, §6	Origin of ICE plots; noted ICE can detect extrapolation	Permute-and-Predict Extrapolation in Variable Importance
Gregorutti, B., Michel, B. & Saint-Pierre, P. (2015). Grouped variable importance with random forests and application to multiple functional data analysis	Computational Statistics & Data Analysis 90, 15-35	§2	Theorem 1 part 1 (PaP = $2{\hat{\beta }}_j^2\sum (x_{ij}-{\bar{x}}_j{)}^2$)	Hooker Mentch Zhou 2021 - Linear Simulation Design and Theorem 1
Fisher, A., Rudin, C. & Dominici, F. (2019). All models are wrong, but many are useful: learning a variable’s importance by studying an entire class of prediction models simultaneously	JMLR 20(177), 1-81	§1, §2, §5	Averaging over all permutations, U-statistic bounds, model class reliance, conditional model reliance	Fisher Rudin Dominici 2019 - Model Class Reliance - Overview
Ishwaran, H. & Lu, M. (2019). Standard errors and confidence intervals for variable importance in random forest regression, classification, and survival	Statistics in Medicine 38(4), 558-582	§1	U-statistic confidence intervals for forest importance	Permute-and-Predict Extrapolation in Variable Importance

2. Evidence of correlation and selection bias in importance

Reference	Venue	Cited in	Role	Vault note
Strobl, C., Boulesteix, A.-L., Zeileis, A. & Hothorn, T. (2007). Bias in random forest variable importance measures: illustrations, sources and a solution	BMC Bioinformatics 8(1), 25	§1	OOB importance biased toward correlated / many-category features; split-improvement bias	Strobl et al 2007 - Bias in RF Variable Importance - Overview
Archer, K. J. & Kimes, R. V. (2008). Empirical characterization of random forest variable importance measures	Computational Statistics & Data Analysis 52(4), 2249-2260	§1	Better performance when signal and noise features are uncorrelated	Permute-and-Predict Extrapolation in Variable Importance
Nicodemus, K. K., Malley, J. D., Strobl, C. & Ziegler, A. (2010). The behaviour of random forest permutation-based variable importance measures under predictor correlation	BMC Bioinformatics 11(1), 110	§1	Large simulation: OOB overestimates correlated predictors	same
Toloşi, L. & Lengauer, T. (2011). Classification with correlated features: unreliability of feature ranking and solutions	Bioinformatics 27(14), 1986-1994	§4	Same pattern in feature ranking	Hooker Mentch Zhou 2021 - Extrapolation Mechanism in Forests and Neural Nets
Díaz-Uriarte, R. & De Andres, S. A. (2006). Gene selection and classification of microarray data using random forest	BMC Bioinformatics 7(1), 3	§1	Backward elimination with forests, the screening use at risk	Permute-and-Predict Extrapolation in Variable Importance
Bénard, C., Da Veiga, S. & Scornet, E. (2021). MDA for random forests: inconsistency, and a practical solution via the Sobol-MDA	arXiv:2102.13347	§7	Analysis of the precise biases of PaP	Hooker Mentch Zhou 2021 - Partial Dependence Alternatives and Conclusions

3. Conditional generation, knockoffs and pseudovariables

Reference	Venue	Cited in	Role	Vault note
Strobl, C., Boulesteix, A.-L., Kneib, T., Augustin, T. & Zeileis, A. (2008). Conditional variable importance for random forests	BMC Bioinformatics 9(1), 307	§5	First conditional permutation scheme (within-partition permutation)	Strobl et al 2008 - Conditional Variable Importance - Overview
Tuv, E., Borisov, A., Runger, G. & Torkkola, K. (2009). Feature selection with ensembles, artificial variables, and redundancy elimination	JMLR 10, 1341-1366	§5	Tree ensembles for predictively non-redundant feature sets	Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures
Wu, Y., Boos, D. D. & Stefanski, L. A. (2007). Controlling variable selection by the addition of pseudovariables	JASA 102(477), 235-243	§5	Pseudovariables to tune linear model size	same
Barber, R. F., Candès, E. J., et al. (2015). Controlling the false discovery rate via knockoffs	Annals of Statistics 43(5), 2055-2085	§5	Knockoff filter; FDR control (augment-and-filter mode)	Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures
Candès, E., Fan, Y., Janson, L. & Lv, J. (2018). Panning for gold: “model-X” knockoffs for high dimensional controlled variable selection	JRSS-B 80(3), 551-577	§1, §5, §5.1	Model-X knockoffs; conditional randomization test; the §5.1 knockoff substitute	same; Hooker Mentch Zhou 2021 - Relearning Hypothesis Tests and Bike-Share Application
Berrett, T. B., Wang, Y., Barber, R. F. & Samworth, R. J. (2020). The conditional permutation test for independence while controlling for confounders	JRSS-B 82(1), 175-197	§7	Hybrid: non-uniform permutations informed by the conditional law	Hooker Mentch Zhou 2021 - Partial Dependence Alternatives and Conclusions
Liu, Y. & Zheng, C. (2018). Auto-encoding knockoff generator for FDR controlled variable selection	arXiv:1809.10765	§7	Learning a model for $x_{ij}\mid x_{i,-j}$	same
Nelsen, R. B. (2007). An introduction to copulas	Springer	§2	Gaussian copula used to correlate $x_1,x_2$	Hooker Mentch Zhou 2021 - Linear Simulation Design and Theorem 1

4. Re-learning and hypothesis tests

Reference	Venue	Cited in	Role	Vault note
Mentch, L. & Hooker, G. (2016). Quantifying uncertainty in random forests via confidence intervals and hypothesis tests	JMLR 17(1), 841-881	§1, §5, §5.1, §7	Permute-and-relearn; first formal RF importance tests	Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures
Mentch, L. & Hooker, G. (2017). Formal hypothesis tests for additive structure in random forests	J. Computational and Graphical Statistics 26(3), 589-597	§1, §6	Permute-and-refit; tests for interactions	same; Hooker Mentch Zhou 2021 - Partial Dependence Alternatives and Conclusions
Mentch, L. & Zhou, S. (2020). Getting better from worse: augmented bagging and a cautionary tale of variable importance	arXiv:2003.03629	§1, §5.1	A permuted feature can improve accuracy in low-signal settings; permute-and-relearn tests over-reject	Hooker Mentch Zhou 2021 - Relearning Hypothesis Tests and Bike-Share Application
Coleman, T., Peng, W. & Mentch, L. (2019). Scalable and efficient hypothesis testing with random forests	arXiv:1904.07830	§5.1	Scalable nonparametric importance test	same
Williamson, B. D., Gilbert, P. B., Simon, N. R. & Carone, M. (2020). A unified approach for inference on algorithm-agnostic variable importance	arXiv:2004.03683	§5.1	Model-agnostic test used in the Fig. 8 simulation	same
Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R. J. & Wasserman, L. (2018). Distribution-free predictive inference for regression	JASA 113(523), 1094-1111	§1, §5	LOCO importance in a conformal-inference framework	Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures; Conformal Prediction - Overview
Lehmann, E. L. & Romano, J. P. (2006). Testing statistical hypotheses	Springer	§5	LOCO as a classical idea	Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures

5. Functional ANOVA, Sobol indices, Shapley and distillation

Reference	Venue	Cited in	Role	Vault note
Hooker, G. (2007). Generalized functional ANOVA diagnostics for high-dimensional functions of dependent variables	J. Computational and Graphical Statistics 16(3)	§1, §6, §7	Source of the extrapolation explanation; generalized fANOVA	Permute-and-Predict Extrapolation in Variable Importance
Sobol, I. M. (1993). Sensitivity analysis for non-linear mathematical models	Mathematical Modelling and Computational Experiment 1, 407-414	§1	PaP importance = Sobol index under independence	Variance-Based Sensitivity and Sobol Indices
Roosen, C. B. (1995). Visualization and exploration of high-dimensional functions using the functional ANOVA decomposition	PhD thesis, Stanford University	§1	Early use of fANOVA to interpret ML functions	Permute-and-Predict Extrapolation in Variable Importance
Chastaing, G., Gamboa, F., Prieur, C., et al. (2012). Generalized Hoeffding-Sobol decomposition for dependent variables: application to sensitivity analysis	Electronic Journal of Statistics 6, 2420-2448	§6	Smoothing-based estimation of generalized fANOVA	Hooker Mentch Zhou 2021 - Partial Dependence Alternatives and Conclusions
Owen, A. B. (2014). Sobol’ indices and Shapley value	SIAM/ASA J. Uncertainty Quantification 2(1), 245-251	§7	Shapley-based importance	Shapley Values and SHAP Value Functions
Lundberg, S. M. & Lee, S.-I. (2017). A unified approach to interpreting model predictions	NeurIPS (31st), 4768-4777	§1, §5, §7	SHAP	Kumar et al 2020 - Problems with Shapley-Value Explanations - Overview
Lou, Y., Caruana, R., Gehrke, J. & Hooker, G. (2013). Accurate intelligible models with pairwise interactions	KDD ‘13, 623-631	§6	Additive models as interpretable surrogates	Hooker Mentch Zhou 2021 - Partial Dependence Alternatives and Conclusions
Tan, S., Caruana, R., Hooker, G., Koch, P. & Gordo, A. (2018a). Learning global additive explanations for neural nets using model distillation	arXiv:1801.08640	§1, §6, §7	Additive-model distillation	same
Tan, S., Caruana, R., Hooker, G. & Lou, Y. (2018b). Distill-and-compare: auditing black-box models using transparent model distillation	AIES ‘18, 303-310	§1, §6, §7	Same	same
Wood, S. N. (2006). Generalized additive models: an introduction with R	Chapman and Hall/CRC	§6	GAM fitting	same

6. Split-improvement corrections

Reference	Venue	Cited in	Role
Zhou, Z. & Hooker, G. (2019). Unbiased measurement of feature importance in tree-based methods	arXiv:1903.05179	§1	Correction for split-improvement bias
Loecher, M. (2020). Unbiased variable importance for random forests	Communications in Statistics - Theory and Methods, 1-13	§1	Same
Li, X., Wang, Y., Basu, S., Kumbier, K. & Yu, B. (2019). A debiased MDI feature importance measure for random forests	arXiv:1906.10845	§1	Same

7. Local explanations, critiques and data

Reference	Venue	Cited in	Role	Vault note
Rudin, C. (2019). Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead	Nature Machine Intelligence 1(5), 206-215	§1	Argues against post hoc explanation altogether	Permute-and-Predict Extrapolation in Variable Importance
Simonyan, K., Vedaldi, A. & Zisserman, A. (2013). Deep inside convolutional networks: visualising image classification models and saliency maps	arXiv:1312.6034	§5	Saliency (gradient) explanations	Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures
Ribeiro, M. T., Singh, S. & Guestrin, C. (2016). “Why should I trust you?”: explaining the predictions of any classifier	KDD ‘16, 1135-1144	§5	LIME	same
Slack, D., Hilgard, S., Jia, E., Singh, S. & Lakkaraju, H. (2020). Fooling LIME and SHAP: adversarial attacks on post hoc explanation methods	AIES ‘20, 180-186	§1, §5	Off-distribution manipulation of SHAP/LIME	Kumar et al 2020 - Problems with Shapley-Value Explanations - Overview
Wachter, S., Mittelstadt, B. & Russell, C. (2017). Counterfactual explanations without opening the black box: automated decisions and the GDPR	Harvard Journal of Law and Technology 31, 841	§7	Counterfactual explanations may share extrapolation problems	Hooker Mentch Zhou 2021 - Partial Dependence Alternatives and Conclusions
Fanaee-T, H. & Gama, J. (2013). Event labeling combining ensemble detectors and background knowledge	Progress in Artificial Intelligence, 1-15	§5.2	Hourly bike-share data (UCI)	Hooker Mentch Zhou 2021 - Relearning Hypothesis Tests and Bike-Share Application

(The source truncates two author lists with “et al.”: Barber et al. 2015 is printed as “Barber, R. F., E. J. Candès, et al.” and Chastaing et al. 2012 as “Chastaing, G., F. Gamboa, C. Prieur, et al.”; the authors shown here are as printed. Some titles are lightly recased, e.g. “Mda”/“sobol-mda” → “MDA”/“Sobol-MDA”, “mdi” → “MDI”, “fdr” → “FDR”, “gdpr” → “GDPR”.)

Examples

Example: tracing a claim to its primary source

The body notes say that “Theorem 1 part 1 is given in Gregorutti et al. (2015) and Fisher et al. (2019)“. The table above gives the venue (CSDA 90, 15-35) and shows that Fisher et al. is the same JMLR paper that introduces model class reliance. A reviewer checking the theorem can go to either source. A reader who wants the variance side of importance, which this paper leaves out, is pointed to Ishwaran & Lu (2019) in Statistics in Medicine.

Connections

• The most-cited strands map to other source sets in this vault: Strobl et al 2007 - Bias in RF Variable Importance - Overview, Strobl et al 2008 - Conditional Variable Importance - Overview, Fisher Rudin Dominici 2019 - Model Class Reliance - Overview, Kumar et al 2020 - Problems with Shapley-Value Explanations - Overview.
• LOCO’s conformal-inference origin: Conformal Prediction - Overview.
• Sobol indices and their estimation: Variance-Based Sensitivity and Sobol Indices.

See Also

• Hooker Mentch Zhou 2021 - Permute-and-Predict Extrapolation - Overview — section map
• Index: Hooker Mentch Zhou 2021