Research map / Learning theory and algorithms / Submodular and game algorithms
Causal meets Submodular: Subset Selection with Directed Information
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use random greedy instead of exhaustive search | sensor placement OPT1 · D1, k=2..8 | runtime: 10 hours for exhaustive search | Helped |
| use SmI-based bound instead of 1/e reference bound | greedy guarantee for OPT1 · D1 | tightness of performance guarantee | Helped |
| random greedy vs exhaustive optimum | OPT1 · D1, k=2..8 | objective value | No clear effect |
| random greedy on non-submodular objective | OPT2 covariate selection · ST, target XOM | objective value | No clear effect |
| positive SmI at greedy locations lifts guarantee above 1/e | OPT1 greedy bound · D1 | guarantee vs 1/e: NSmI 0.382 at k=2 to 0.074 at k=8 | Helped |
| sign of SmI varies across k | OPT2 greedy bound · ST | guarantee vs 1-1/e: NSmI -0.305 at k=2, 0.092 at k=8 | Mixed |
| greedy covariate selection for structure learning, small network | causal structure learning · D1 (15 processes) | edge recovery: only the edge 6 -> 4 is miss detected | Helped |
| greedy covariate selection for structure learning, larger network | causal structure learning · D2 (35 processes) | edge recovery (%): 82.69% | Helped |
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