Index: Janzing et al 2020 - Feature Relevance as a Causal Problem

Janzing et al 2020 - Feature Relevance as a Causal Problem

Routing Summary

This folder fully captures Janzing, Minorics & Blöbaum (AISTATS 2020), which argues that Shapley-value attributions should drop features with marginal (interventional) rather than observational conditional expectations. Contains 8 notes spanning attribution axioms, conditional vs marginal value functions, the failure of sensitivity under conditioning, the inputs-as-causes argument, the symmetry debate, and the KernelSHAP vs SHAPR experiments. It is the vault’s owner for interventional vs observational feature relevance.

• Need the paper map, findings and section-by-section source map? → Janzing et al 2020 - Feature Relevance as a Causal Problem - Overview
• Need the attribution axioms (completeness, sensitivity, …), integrated gradients or Theorem 1? → Janzing 2020 - Baseline Attribution Axioms and Integrated Gradients
• Need the definitions of conditional (eq. 3) vs marginal (eq. 4) SHAP, or the back-door eq. (5)? → Janzing 2020 - Conditional vs Marginal Dropping of Features
• Need proof that conditional SHAP credits unused features (Example 1, Lemma 1)? → Janzing 2020 - Irrelevant-Feature Example and Failure of Sensitivity
• Need why $\mathbb{E}[Y\mid do(X_T=x_T)]=\mathbb{E}f(x_T,X_{\bar{T}})$, and why it is model-level only? → Janzing 2020 - Inputs as Causes - Interventional Equals Marginal Expectation
• Need the symmetry-axiom objection (Sundararajan & Najmi Ex. 4.9) and reply? → Janzing 2020 - Symmetry Axiom Objection and Reply
• Need KernelSHAP’s weighted least squares, the Aas et al. kernel estimator, or the simulation designs? → Janzing 2020 - KernelSHAP vs SHAPR Experiments
• Need limitations, model-vs-world guidance, or marketing implications? → Janzing 2020 - Conclusions, Limitations and Model-vs-World Attribution

Concept Map

Concept	Note	Type	Depends On	Key Result
Five attribution properties	Janzing 2020 - Baseline Attribution Axioms and Integrated Gradients	definition	—	Completeness, Sensitivity, Impl. Invariance, Linearity, Symmetry
Theorem 1 (path methods)	Janzing 2020 - Baseline Attribution Axioms and Integrated Gradients	theorem	five properties	First four ⇒ convex combo of path methods; IG unique symmetric path
Shapley value of set function, eq. (2)	Janzing 2020 - Baseline Attribution Axioms and Integrated Gradients	definition	—	${\varphi }_i={\sum }_T[n(\genfrac{}{}{0ex}{}{n-1}{|T|}){]}^{-1}C(i\mid T)$, $\sum {\varphi }_i=g(U)$
Conditional vs marginal simplified function, eq. (3)-(4)	Janzing 2020 - Conditional vs Marginal Dropping of Features	definition	eq. (2)	SHAP theory uses (3), code uses (4)
Back-door adjustment, eq. (5), Fig. 1	Janzing 2020 - Conditional vs Marginal Dropping of Features	theorem	DAGs and Causal Identification	Intervention breaks dependence on $X_1$, keeps $X_2$-$X_3$ dependence
Example 1 / Lemma 1	Janzing 2020 - Irrelevant-Feature Example and Failure of Sensitivity	theorem/example	eq. (3)	Conditional: ${\varphi }_2=x_1/2-1/4\ne 0$; marginal: ${\varphi }_2=0$
Interventional = marginal, eq. (14), Fig. 2	Janzing 2020 - Inputs as Causes - Interventional Equals Marginal Expectation	theorem	eq. (5)	$\mathbb{E}[Y\mid do(X_T=x_T)]=\mathbb{E}f(x_T,X_{\bar{T}})$
Symmetry objection and reply, Fig. 3	Janzing 2020 - Symmetry Axiom Objection and Reply	example	five properties	Credit $1-p$ vs $1-q$; $\tilde{g}$ itself asymmetric
Shapley kernel WLS, eq. (15)	Janzing 2020 - KernelSHAP vs SHAPR Experiments	definition/algorithm	eq. (2)	$k(U,T)=(|U|-1)/[(\genfrac{}{}{0ex}{}{|U|}{|T|})|T|(|U|-|T|)]$
Aas et al. kernel conditional estimator	Janzing 2020 - KernelSHAP vs SHAPR Experiments	algorithm	eq. (3)	Mahalanobis-weighted average of $f$
Gaussian and HAR experiments, Figs. 4-5	Janzing 2020 - KernelSHAP vs SHAPR Experiments	example	linear ground truth	Marginal errors near 0 (spikes about 1,750 / 4,500 / 1,220); conditional dispersed over $\pm 0.5$ (Gaussian) or $\pm 0.10$ (HAR)
Model-vs-world decision rule	Janzing 2020 - Conclusions, Limitations and Model-vs-World Attribution	concept	eq. (14)	Marginal for model use; neither for real causal effects

Notes

• Janzing et al 2020 - Feature Relevance as a Causal Problem - Overview — CONTAINS: research question, contribution, key findings, argument diagram, full Source Map, complete 27-entry reference list grouped by role, one-case worked example, positioning vs Kumar/Strobl/Hooker/Dillon, marketing relevance
• Janzing 2020 - Baseline Attribution Axioms and Integrated Gradients — CONTAINS: §1 motivation, problem set-up and paper plan (uniqueness claim, Datta et al. support); §2 prior work; integrated gradients eq. (1); five properties; Theorem 1; Shapley set function eq. (2); baseline set function; worked IG vs Shapley example
• Janzing 2020 - Conditional vs Marginal Dropping of Features — CONTAINS: notation; eq. (3)-(4); Lundberg & Lee’s justification; footnote 3; Fig. 1 with drawn edges and node colouring; back-door eq. (5) with proof sketch; two structural observations; media-planning illustration
• Janzing 2020 - Irrelevant-Feature Example and Failure of Sensitivity — CONTAINS: Example 1 eq. (6)-(13); completed ${\varphi }_1,{\varphi }_2$ at (1,1) and (0,0); Lemma 1 with proof (printed $X_{\bar{T}}$ typo flagged); sensitivity-paradox resolution via $\tilde{g}$; general proxy-credit mechanism; marketing illustration
• Janzing 2020 - Inputs as Causes - Interventional Equals Marginal Expectation — CONTAINS: inputs-as-causes framing; true features vs inputs; Fig. 2 (five-feature drawing, cut edges, caption); eq. (14) with proof sketch; corollary on interventional Shapley values; footnote 4; licensed-vs-not table; confounded MMM example
• Janzing 2020 - Symmetry Axiom Objection and Reply — CONTAINS: Fig. 3 table; Ex. 4.9 objection; verification ${\varphi }_1=1-p$; two-part reply; $\tilde{g}$ definition; full $\tilde{g}$ table and contributions $C(j\mid T)$; additive-model generalisation; comment on axiom levels; channel illustration
• Janzing 2020 - KernelSHAP vs SHAPR Experiments — CONTAINS: eq. (15) Shapley kernel; KernelSHAP sampling algorithm; eq. (16); linear ground truth; Gaussian conditional formulas; $n=3$/$n=10$ design table; Fig. 4 with read-off values and pooling counts; Aas et al. 3-step estimator; HAR design table; Fig. 5 with read-off values; editorial assessment; audit recipe
• Janzing 2020 - Conclusions, Limitations and Model-vs-World Attribution — CONTAINS: §5 claims; acknowledgements; scope limits; limitations table; “true to the model vs true to the data” framing; decision rule; SHAP-mass model-selection anti-pattern; co-flighting example

Sources

• Janzing et al 2020 - Feature Relevance Quantification in Explainable AI - A Causal Problem — Janzing, Minorics & Blöbaum, AISTATS 2020 (PMLR 108), arXiv:1910.13413v2, 11 pp.

See Also

• Kumar et al 2020 - Problems with Shapley-Value Explanations - Overview — owner of Shapley/SHAP definitions; conditional-vs-interventional catch-22
• Dillon et al - SHAP and Causal Insights - Overview — SHAP is not causal evidence about the world
• Hooker Mentch Zhou 2021 - Permute-and-Predict Extrapolation - Overview — off-manifold extrapolation cost of marginal schemes
• Strobl et al 2008 - Conditional Variable Importance - Overview — conditional permutation importance (the data-level analogue)
• Fisher Rudin Dominici 2019 - Model Class Reliance - Overview — attribution across the Rashomon set
• DAGs and Causal Identification — back-door criterion