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Knockoffs Inference for Partially Linear Models with Automatic Structure Discovery
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Proposes KI-LAND, a knockoffs-based variable selection method for partially linear models that controls FDR separately for linear and nonlinear covariate effects, with FDR and power theory and simulation experiments.
Problem
Variable selection in partially linear / additive models lacks false discovery rate control, and existing knockoff methods do not jointly control FDR for linear and nonlinear effects or give power guarantees for nonlinear settings.
Approach
Combines model-X or deep knockoffs with a LAND-style penalized RKHS (Sobolev) regression that separately penalizes linear and nonlinear components, uses subsampling selection frequencies as knockoff statistics, and applies knockoff thresholds to select linear and nonlinear variable sets with FDR and power guarantees.
Key results
- On simulated data with target FDR 0.2, KI-LAND keeps FDR at or below the nominal level across sample sizes, dimensions and correlations, while LAND inflates FDR (e.g., 0.3333 at n=50).
- KI-LAND's linear-set power is around 50-90% across settings, with nonlinear-set power of 40-90%, and is lower than KKO (up to 95%) but KKO cannot distinguish linear from nonlinear variables.
- Theorem 1 gives mFDR/FDR control for any n and d; Theorem 2 gives power tending to 1 as n grows under minimum-signal and incoherence assumptions.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use KI-LAND to select linear and nonlinear variables | KI-LAND · Simulated data, varying sample size | power | Helped |
| Increase the variable dimension | KI-LAND · Simulated data, varying variable dimension | power | Hurt |
| Increase the correlation between variables | KI-LAND · Simulated data, varying correlation | power | Hurt |
| Use KI-LAND instead of LAND | Simulated data, n=200, d=100, ρ=0.2 · Simulated data, n=200, d=100, ρ=0.2 | FDR: 0.3182 -> 0.2000 | Helped |
| Use KKO instead of KI-LAND | Simulated data, n=200, d=100, ρ=0.2 · Simulated data, n=200, d=100, ρ=0.2 | power: 90.00% -> 80.00% | Hurt |
| Use Model-X for nonlinear relationships | Simulated data · Simulated data | power | Hurt |
Surprising findings
- KI-LAND has weaker power than KKO in the reported simulations, although it additionally identifies linear versus nonlinear variables.
Limitations
- Power of the procedure is lower than KKO in the reported experiments.
- Theoretical guarantees rely on strong assumptions such as irrepresentable and mutual incoherence conditions and oracle selection.
- Experiments are limited to simulated data in the main text; real-world results are deferred to the supplement.
Experimental setup
Datasets: simulated data
Benchmarks: simulated PLM data with d=50-400 and n=50-400
Metrics: FDR power
Baselines: LAND KKO Model-X knockoffs
Builds on: model-X knockoffs LAND kernel knockoffs (KKO) deep knockoffs stability selection
Closest papers by meaning
- Integral-based Knockoffs Inference for Partially Linear Models (AAAI 2026 · similarity 0.92)
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- Semi-knockoffs: a model-agnostic conditional independence testing method with finite-sample guarantees (ICML 2026 · similarity 0.86)
- Power analysis of knockoff filters for correlated designs (NeurIPS 2019 · similarity 0.84)
- Importance Sampling for Nonlinear Models (ICML 2025 · similarity 0.82)
- An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds (NeurIPS 2025 · similarity 0.82)
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