Index: Hooker Mentch Zhou 2021 - Permute-and-Predict Extrapolation

Hooker Mentch Zhou 2021 - Permute-and-Predict Extrapolation

Routing Summary

This folder fully captures Hooker, Mentch & Zhou (2021), Unrestricted permutation forces extrapolation (Statistics and Computing 31:82; arXiv:1905.03151v2), in 8 notes. The topics are permute-and-predict (PaP) importance, PDP and ICE; why random forests and neural nets inflate correlated features; Theorems 1-3; the conditional, LOCO, permute-and-relearn and condition-and-relearn alternatives; test-size inflation; the bike-share example; and alternatives for effect plots.

• Need the paper’s thesis, findings, or section map? → Hooker Mentch Zhou 2021 - Permute-and-Predict Extrapolation - Overview
• Need definitions of ${\mathrm{VI}}^{\pi }$, PD, ICE, or their population targets? → Permute-and-Predict Extrapolation in Variable Importance
• Need what PaP returns for a linear model (Theorem 1) or the simulation design and rank results? → Hooker Mentch Zhou 2021 - Linear Simulation Design and Theorem 1
• Need why forests and NNs extrapolate (potential nearest neighbours, Gibbs-like variance)? → Hooker Mentch Zhou 2021 - Extrapolation Mechanism in Forests and Neural Nets
• Need a non-extrapolating importance measure, Theorems 2-3, or the compensation effect? → Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures
• Need to test importance, or a real-data example? → Hooker Mentch Zhou 2021 - Relearning Hypothesis Tests and Bike-Share Application
• Need safer effect plots or the paper’s conclusions? → Hooker Mentch Zhou 2021 - Partial Dependence Alternatives and Conclusions
• Need a cited work’s venue, the funding, or the reference list? → Hooker Mentch Zhou 2021 - References and Acknowledgments

Concept Map

Concept	Note	Type	Depends On	Key Result
Permutation importance ${\mathrm{VI}}_j^{\pi }$	Permute-and-Predict Extrapolation in Variable Importance	definition	—	Loss increase after marginal permutation of $x_j$
PD / ICE	Permute-and-Predict Extrapolation in Variable Importance	definition	—	${\mathrm{PD}}_j(x)=\frac{1}{N}{\sum }_{i}f(x_i^{x,j})$
PaP population targets	Permute-and-Predict Extrapolation in Variable Importance	definition	—	Integrate against marginal $p_j$
Functional ANOVA, eq. (1)	Permute-and-Predict Extrapolation in Variable Importance	definition	Variance-Based Sensitivity and Sobol Indices	PaP VI = Sobol index under independence
Theorem 1	Hooker Mentch Zhou 2021 - Linear Simulation Design and Theorem 1	theorem	PaP definitions	$E_{\pi }{\mathrm{VI}}_j^{\pi }=2{\hat{\beta }}_j^2\sum (x_{ij}-{\bar{x}}_j{)}^2$
Copula simulation, eq. (2)	Hooker Mentch Zhou 2021 - Linear Simulation Design and Theorem 1	example	Copula Estimation	RF/NN inflate $x_1,x_2$ at $\rho =0.9$; linear model does not
Potential nearest neighbours, eq. (3)	Hooker Mentch Zhou 2021 - Extrapolation Mechanism in Forests and Neural Nets	definition	Honest Trees and Causal Forests	Off-data points average distant leaves
${\mathrm{VI}}^C,{\mathrm{VI}}^D,{\mathrm{VI}}^{\pi L},{\mathrm{VI}}^{CL}$	Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures	definition	PaP definitions	Need “one more model”
Theorem 2	Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures	theorem	Regression and the CEF	Shared target $E(f-E[f\mid x_{-j}]{)}^2$
Theorem 3 / compensation	Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures	theorem	Omitted Variables Bias	Importance $\propto {\beta }_j^2\sum {\delta }_{ij}^2$
Ordering vs testing	Hooker Mentch Zhou 2021 - Relearning Hypothesis Tests and Bike-Share Application	example	Theorem 2	Permute-and-relearn tests over-reject; knockoffs about 5%
Bike-share ranks	Hooker Mentch Zhou 2021 - Relearning Hypothesis Tests and Bike-Share Application	example	—	temp OOB rank 10 → relearn rank 1; yr 6 → 11
Model class reliance (as used here)	Permute-and-Predict Extrapolation in Variable Importance	definition	Fisher Rudin Dominici 2019 - Model Class Reliance - Overview	Profile-CI analogue; prefer conditional version
Knockoff modes	Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures	definition	—	Swap-and-test (CRT) vs augment-and-filter (FDR)
Generalized fANOVA PD	Hooker Mentch Zhou 2021 - Partial Dependence Alternatives and Conclusions	definition	eq. (1)	Minimize $\int (f-f_1-f_{-1}{)}^{2}p(x)dx$

Notes

• Hooker Mentch Zhou 2021 - Permute-and-Predict Extrapolation - Overview — CONTAINS: citation; thesis; contributions (i)-(iii); key-findings table; full Source Map (§1-§7, App. A); pregnant-men example; correlated media-channel illustration.
• Permute-and-Predict Extrapolation in Variable Importance — CONTAINS: “X-ray the black box” framing and Rudin (2019); notation; definitions of ${\mathrm{VI}}_j^{\pi }$ (incl. OOB), ${\mathrm{PD}}_j$, ${\mathrm{ICE}}_{i,j}$; literature on correlation bias; two-effects distinction; population targets ${\mathrm{VI}}_j^{\pi }(f)$, $f_{-j}$, $f_j$; linear yardstick; backward-elimination danger; inference vs model audit; model class reliance definition (profile-CI analogue); scope statement (algorithm class, model-agnostic, Shapley more complex); remedies preview and “gold standard” quote; functional ANOVA eq. (1); Shapley and split-improvement remarks.
• Hooker Mentch Zhou 2021 - Linear Simulation Design and Theorem 1 — CONTAINS: eq. (2) model; design logic; Theorem 1 + proof sketch; caveat on unhatted PD/ICE constants; simulation protocol (algorithm); theoretical ranks; full Fig. 1 table (every series × feature, both panels); Fig. 2 caption check, design grid and full four-panel rank tables; Fig. 3 PD, PD-SD and ICE readings with line-type caveat; worked Theorem 1 example.
• Hooker Mentch Zhou 2021 - Extrapolation Mechanism in Forests and Neural Nets — CONTAINS: two-feature experiment setup (noise SD 0.05, SNR = 100/3 derivation); Fig. 4 three panels; Fig. 4 contour-level readings table and leaf-boundary description; eq. (3) tree weights and pNN definition; pNN mechanism; joint-inflation claim; NN variance and Gibbs effects; Fig. 5 mean/SD contour readings table; Fig. 6 PD/ICE readings table; seasonal-driver illustration.
• Hooker Mentch Zhou 2021 - Conditional and Relearning Importance Measures — CONTAINS: the two families of alternatives; the two knockoff modes; definitions of ${\mathrm{VI}}^C,{\mathrm{VI}}^D,{\mathrm{VI}}^{\pi L},{\mathrm{VI}}^{CL}$; sign-convention note; condition-and-relearn algorithm; Theorem 2 + proof; how ${\mathrm{VI}}^D$ fits Theorem 2 (constant replacement); full Fig. 7 tables (all six panels, every measure × feature); Theorem 3 + proof; Theorem 3 notation caveats ($\hat{\gamma }$ vs $\gamma$, ${\hat{\beta }}_j$ vs ${\beta }_j$, factor 2); compensation effect; joint importance; local explanations (saliency, LIME, SHAP) and the threshold counterexample; collinear-channels example.
• Hooker Mentch Zhou 2021 - Relearning Hypothesis Tests and Bike-Share Application — CONTAINS: generic importance $H_0$; Mentch & Zhou (2020) finding; noise-feature test simulation design; full Fig. 8 rejection-rate tables (all SNR × model × $q$; knockoff and truth ranges; Monte Carlo SE); ordering-vs-testing claim; bike-share setup and full Fig. 9 rank table (approx.); target-leakage remark.
• Hooker Mentch Zhou 2021 - References and Acknowledgments — CONTAINS: affiliations; NSF grants and computing acknowledgment; all 46 references with venues, grouped by role (PaP origins, bias evidence, conditional/knockoff, re-learning tests, fANOVA/Shapley/distillation, split-improvement corrections, local explanations and data), each mapped to citing section and vault note.
• Hooker Mentch Zhou 2021 - Partial Dependence Alternatives and Conclusions — CONTAINS: restricted ICE; caution on averaging supported segments; generalized fANOVA projection (definition); Chastaing smoothing; GAM distillation (formal additive-model definition, distillation algorithm, link to generalized fANOVA); §7 conclusions 1-5; limitations; MMM response-curve illustration.

Sources

• Hooker Mentch Zhou 2021 - Unrestricted Permutation Forces Extrapolation — Hooker, Mentch & Zhou (2021), arXiv:1905.03151v2, 22 pp.

See Also

• Strobl et al 2007 - Bias in RF Variable Importance - Overview — split-selection bias (different mechanism)
• Strobl et al 2008 - Conditional Variable Importance - Overview — conditional permutation within tree partitions
• Fisher Rudin Dominici 2019 - Model Class Reliance - Overview — model reliance and the Rashomon set
• Kumar et al 2020 - Problems with Shapley-Value Explanations - Overview — off-manifold SHAP
• Janzing et al 2020 - Feature Relevance as a Causal Problem - Overview — interventional vs observational relevance
• Meinshausen Buhlmann 2010 - Stability Selection - Overview — stable selection under noisy importances