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DeepDRK: Deep Dependency Regularized Knockoff for Feature Selection
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Proposes DeepDRK, a transformer-based deep knockoff generator trained adversarially with multiple swappers and a sliced-Wasserstein correlation penalty, plus a post-training dependency-regularized perturbation, to improve FDR-controlled feature selection on non-Gaussian data.
Problem
Deep Model-X knockoff generators struggle to satisfy the swap property at the sample level, leading to overfitting, high reconstructability/collinearity, and low power, especially with small samples and non-Gaussian data.
Approach
Formulate knockoff generation as a min-max game against multiple neural swappers (multi-swapper adversarial attacks with a swapper diversity penalty and REx variance term), add a sliced Wasserstein correlation regularizer to reduce dependence between X and knockoffs, and post-hoc mix the knockoff with a row-permuted copy of X to further cut reconstructability.
Key results
- At n=200 on the Gaussian mixture setup, DeepDRK achieves mean FDR 0.116 versus 0.390 (KnockoffGAN), 0.720 (sRMMD), 0.735 (Deep Knockoff), and 0.772 (DDLK), at the cost of lower power (0.791 vs ~0.97-1.0 for baselines).
- At n=2000 on the Gaussian mixture setup, DeepDRK reaches mean FDR 0.081 with power 0.973, while Deep Knockoff and sRMMD have FDR above 0.63.
- On the IBD case study, DeepDRK identifies 23 metabolites of which 19 are literature-referenced, the most among compared models.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DeepDRK instead of KnockoffGAN | Gaussian mixture feature selection · Gaussian mixture, n=200 | FDR mean: 0.390 -> 0.116 | Helped |
| Use DeepDRK instead of KnockoffGAN | Gaussian mixture feature selection · Gaussian mixture, n=200 | Power mean: 0.971 -> 0.791 | Hurt |
| Use DeepDRK instead of KnockoffGAN | Gaussian mixture feature selection · Gaussian mixture, n=2000 | FDR mean: 0.118 -> 0.081 | Helped |
| Use DeepDRK instead of KnockoffGAN | Gaussian mixture feature selection · Gaussian mixture, n=2000 | Power mean: 0.973 -> 0.973 | No clear effect |
| Decrease the DRP perturbation weight αₙ (ablation) | DeepDRK · Five synthetic datasets, n=2000 | Power | Helped |
| Vary the DRP perturbation weight αₙ (ablation) | DeepDRK · Five synthetic datasets, n=2000 | FDR | Mixed |
Surprising findings
- Competing objectives: minimizing the swap loss and the dependency loss trade off during training, so Type I and Type II error cannot both be reduced at the sample level.
- Baseline deep knockoff models achieve high power but FDR well above the nominal 0.1 level in small-sample synthetic settings.
Limitations
- FDR exceeds the 0.1 threshold in some small-sample (n=200) settings.
- Perturbation weight alpha_n is set heuristically (0.5) and may not be optimal; no theory on swap property and power for the full method.
- Real-data case study has no ground truth and relies on literature-based qualitative evaluation.
Experimental setup
Datasets: synthetic Gaussian mixture Clayton and Joe copula synthetic data 10x Genomics scRNA-seq IBD metabolomics (Metabolomics Workbench)
Benchmarks: synthetic Gaussian mixture copula synthetic semi-synthetic scRNA-seq semi-synthetic IBD metabolomics IBD case study
Metrics: FDR power literature-supported metabolites identified
Baselines: Deep Knockoff DDLK KnockoffGAN sRMMD
Builds on: Model-X knockoffs DDLK Deep Knockoff DeepPINK Vision Transformer
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