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

arXiv: https://arxiv.org/abs/2608.00989 · HTML: https://mlsanity.com/paper/2608.00989/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 60 references that are in the map.
- First posted on arXiv 2 Aug 2026.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [TokenSHAP: Interpreting Large Language Models with Monte Carlo Shapley Value Estimation](https://mlsanity.com/paper/2407.10114/) (2024)
- [DeepPINK: reproducible feature selection in deep neural networks](https://mlsanity.com/paper/1809.01185/) (2018)
- [De-biasing the Lasso: Optimal Sample Size for Gaussian Designs](https://mlsanity.com/paper/1508.02757/) (2015)
- [Consistent Feature Selection for Analytic Deep Neural Networks](https://mlsanity.com/paper/2010.08097/) (2020)
- [CausalRivers -- Scaling up benchmarking of causal discovery for real-world time-series](https://mlsanity.com/paper/2503.17452/) (2025)
- [A knockoff filter for high-dimensional selective inference](https://mlsanity.com/paper/1602.03574/) (2016)
- [Interpretation of Prediction Models Using the Input Gradient](https://mlsanity.com/paper/1611.07634/) (2016)
- [AFS: An Attention-based mechanism for Supervised Feature Selection](https://mlsanity.com/paper/1902.11074/) (2019)
- [Neural Granger Causality](https://mlsanity.com/paper/1802.05842/) (2018)
- [False Discovery Rate Control via Data Splitting](https://mlsanity.com/paper/2002.08542/) (2020)
- [The knockoff filter for FDR control in group-sparse and multitask regression](https://mlsanity.com/paper/1602.03589/) (2016)
- [Metropolized Knockoff Sampling](https://mlsanity.com/paper/1903.00434/) (2019)
- [Controlling False Discovery Rate Using Gaussian Mirrors](https://mlsanity.com/paper/1911.09761/) (2019)
- [A Scale-free Approach for False Discovery Rate Control in Generalized Linear Models](https://mlsanity.com/paper/2007.01237/) (2020)
- [Normalizing Flows for Knockoff-free Controlled Feature Selection](https://mlsanity.com/paper/2106.01528/) (2021)
- [High-Dimensional Knockoffs Inference for Time Series Data](https://mlsanity.com/paper/2112.09851/) (2021)
- [FDR-Controlled Portfolio Optimization for Sparse Financial Index Tracking](https://mlsanity.com/paper/2401.15139/) (2024)
- [Neural Gaussian Mirror for Controlled Feature Selection in Neural Networks](https://mlsanity.com/paper/2010.06175/) (2020)

## Abstract (arXiv)

Most FDR-controlled feature selection methods are designed for coordinate-wise hypotheses, where each feature has a single weight or importance score. This abstraction fails in sequential and grouped models, where one original feature is represented by a block of sub-features, such as lags, recurrent states, or attention-based interactions. We propose a grouped-feature FDR control framework for such settings. For grouped linear models, we construct null-symmetric block-level mirror statistics with matrix-valued perturbations. For neural sequential models, we combine Permutation SHAP derivatives as model-agnostic block-level importance scores with kernel-based dependence measure. The framework is model-agnostic across network architectures, does not require specifying the covariate distribution, and reduces to Gaussian Mirror or Neural Gaussian Mirror when the block size is one. We prove FDR control for low- and high-dimensional grouped linear models and asymptotic symmetry of smoothed Permutation SHAP derivatives under fixed fitted nonlinear models. Experiments on simulated and real-world datasets show reliable FDR control and improved power under correlated grouped-feature signals.