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Model-Agnostic FDR Control via Group Gaussian Mirror and Permutation SHAP

NeurIPS 2026 · Learning theory and algorithms › Kernels and regression theory · approach: Kernel regression under shift · 0 citations (OpenAlex)

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Extends Gaussian Mirror and Neural Gaussian Mirror FDR control from single-weight to grouped (block) feature hypotheses, using block-level mirror statistics for linear models and Permutation SHAP derivatives for LSTM/GRU/Transformer models.

Problem

FDR-controlled feature selection assumes one feature has one weight, which fails for grouped or sequential models where a feature is a block of sub-features (lags, hidden states, attention channels); the grouped null requires all block weights to vanish jointly.

Approach

Lifts Gaussian Mirror to block-valued mirror variables X_j ± Z̃_j G_j with block-orthogonality for linear models, and for neural sequential models uses smoothed Permutation SHAP derivatives aggregated per block as importance scores within a kernel conditional-dependence objective for optimizing the perturbation matrix.

Key results

• Linear AR grouped simulations (n=2500, p*m=1500): GGM-OLS FDR 0.020-0.135 with power ~1.0 at q=0.1, while Group Lasso FDR 0.37-0.46.
• LSTM simulations (p*m=1500, weak signal): PSGM FDR 0.161 with power 0.879 vs. Fitted Derivative FDR 0.213 and power 0.842; AGL power 0.966 but FDR 0.916.
• CausalRivers semi-synthetic y with Transformer: PSGM FDR 0.258 and power 0.897 versus AGL FDR 0.772.

Surprising findings

• Group Lasso and AGL-type selection have FDR far above target q=0.1 in most settings, and on real CausalRivers y AGL selects 100% null groups in proxy terms.
• On real CausalRivers data PSGM's proxy FDR (0.576) is not controlled at q=0.2 in some settings, and Sawaya's method has lower FDR but much lower power.

Limitations

• Neural version depends on the quality of the fitted predictive model and may lose null symmetry under spurious correlations.
• Performs best with moderate block size and sparse support; less conservative FDR control in some settings.
• Real-data FDR and power are only graph-proxy metrics since the river graph does not define the statistical null.

Experimental setup

Datasets: CausalRivers simulated AR grouped design simulated latent logistic factor design

Benchmarks: CausalRivers

Metrics: FDR power test MSE

Baselines: Group Lasso Partial-F BH AGL AFS Sawaya data-splitting Fitted Derivative

Builds on: Gaussian Mirror Neural Gaussian Mirror Permutation SHAP Group Lasso Benjamini-Hochberg

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