Research map / Learning theory and algorithms / Matrix and tensor methods
Sparse + Group-Sparse Dirty Models: Statistical Guarantees without Unreasonable Conditions and a Case for Non-Convexity
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace clean sparse or group-sparse regularizers with convex sparse + group-sparse dirty model | multitask molecular activity regression · Molecular activity (3 tasks) | average R2: 0.43 vs best clean baseline 0.38 (GMCP) | Helped |
| Use non-convex (SCAD/MCP) group-sparse dirty penalties instead of convex dirty penalties | sparse + group-sparse dirty multitask model · Molecular activity (3 tasks) | average R2: 0.49 vs 0.43 for convex dirty model | Helped |
| Use non-convex dirty penalties instead of convex dirty penalties | simulated multitask regression, varying sample size · Simulated multitask (m=10, p=260) | l-infinity error | Helped |
| Surrogate-component construction (decomposable error vectors) to remove structural incoherence requirement for convex sparse + group-sparse model | convex sparse + group-sparse dirty model · theory (l2 consistency, Theorem 1) | l2 error bound | Helped |
| Non-convex penalties instead of convex penalties | sparse + group-sparse dirty model · theory (support recovery, l-infinity) | required incoherence and sample size | Helped |
| Use non-convex unbiased regularizers instead of convex ones | l2 estimation error rate · theory | asymptotic l2 convergence rate | No clear effect |
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