Simulation study: the thesis method on known truth

1. Background

This is the simulation study from Chapter 4 of the thesis, the foundation the method was built on. Real biological data can't tell you which features are truly causal, so the thesis built a synthetic world where the truth is known: three blocks of ten correlated features drive a binary outcome, buried in hundreds of noise features. Five methods competed on identical data: baseline lasso, early and late fusion with standard correlation-rank penalties, and early and late fusion with the adaptive surprisal weights. The numbers below are the thesis's reported results.

2. Setup

Eighteen scenarios: sample size 100 or 200, noise features 200, 300, or 400, and causal effect multipliers of 1.0, 1.5, or 2.0. Fifty independent runs per scenario. Each dataset: three causal blocks of ten correlated features (30 true signals), a binary outcome drawn from a logistic model on the three latent block drivers, plus the noise matrix. Groups were learned by hierarchical clustering, not given to the method. Metrics are averaged over all scenarios and runs.

3. Results

Method	FDR	Sensitivity	F1	Stability (Jaccard)
Baseline LASSO	0.526	0.159	—	0.058
Early fusion, standard	0.72	high	—	0.24
Late fusion, standard	0.81	high	—	0.33
Late fusion, adaptive	0.387	0.85	0.674	0.389
Early fusion, adaptive	0.01	0.67	0.787	0.59

False discovery rate by method, averaged over all 18 simulation scenarios (50 runs each). Lower is better.

Selection stability by method: mean pairwise Jaccard of the selected sets across runs. Higher is better.

The adaptive weights did their job. Early fusion with adaptive weights held the false discovery rate to 0.01 while recovering two-thirds of the true signals, giving the best F1 (0.787) and the best selection stability (Jaccard 0.59) with a parsimonious set of about 30 features. Late fusion with adaptive weights was the most sensitive method (0.85, perfect recovery of the strongest block) but admitted far more noise (FDR 0.387), which dragged its F1 to 0.674.

The standard penalties, which weight groups only by within-group correlation, drowned in false discoveries: FDR 0.72 for early fusion, 0.81 for late fusion, despite high sensitivity. And the baseline lasso fractured under high-dimensional noise: FDR 0.526, sensitivity 0.159, near-zero stability (0.058).

Reading the table. Dashes mean the thesis text does not report that metric numerically; "high" is the thesis's own description of the standard arms' sensitivity. All numbers above are quoted from Chapter 4.

4. Takeaway

The simulation established two things before the method ever touched real data. First, the adaptive surprisal weights work: they suppress the noise floor while letting true signal groups through, which is why early-fusion adaptive was the most precise and most reproducible method in the study. Second, fusion architecture matters: early fusion's joint penalty beat late fusion's isolated models on precision and stability, at some cost in raw sensitivity. Those are the results the TCGA-BRCA study was designed to check on real biology. (The SKAT correction described on the Methods page concerns the real-data application, where SKAT choked on standardized expression values; in these simulations the weights behaved as designed.)