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Exact and Efficient Inference for Collective Flow Diffusion Model via Minimum Convex Cost Flow Algorithm
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace L-BFGS-B (lambda=1) with the min convex cost flow method | MAP inference · synthetic Dirichlet, F=10^4, L=30 | avg running time (s): 357.32 (39.76) -> 4.54 (0.16) | Helped |
| replace L-BFGS-B (lambda=1) with the proposed method | MAP inference · synthetic Exponential decay, L=20, F=10^5 | avg running time (s): >1000.00 (−) -> 2.44 (0.58) | Helped |
| increase penalty lambda from 1 to 100 (ablation) | L-BFGS-B · synthetic Dirichlet, F=10^4, L=20 | avg running time (s): 132.86 (15.46) -> 169.83 (17.19) | Hurt |
| increase penalty lambda from 1 to 100 (ablation) | L-BFGS-B · synthetic Dirichlet, L=20, F=10^5 | avg running time (s): 434.25 (114.80) -> 793.54 (146.68) | Hurt |
| increase grid size L from 10 to 30 | Proposed · synthetic Dirichlet, F=10^4 | avg running time (s): 0.05 (0.00) -> 4.54 (0.16) | Hurt |
| increase total population F from 10^4 to 10^6 | Proposed · synthetic Dirichlet, L=20 | avg running time (s): 0.71 (0.09) -> 14.25 (1.56) | Hurt |
| increase lambda from 1 to 100 on real data (ablation) | L-BFGS-B · real data April 1st 2015, 5km | avg running time (s): 196.46 (139.61) -> 2.04 (0.73) | Helped |
| use the proposed method instead of L-BFGS-B (lambda=100) at 5km | MAP inference · real data April 1st 2015, 5km | avg running time (s): 2.04 (0.73) -> 0.84 (0.16) | Hurt |
| use the proposed method instead of L-BFGS-B at 1km cells | MAP inference · real data April 1st 2015, 1km | avg running time (s): >1000.00 (−) -> 59.40 (22.38) | Helped |
| use proposed exact solver instead of continuous relaxation L-BFGS-B | MAP inference · synthetic Exponential decay, L=5, F=10^2 | solution sparsity: 0% -> 90% | Helped |
| use proposed method instead of L-BFGS-B in EM algorithm | EM algorithm · synthetic grid, L=12 | time to reach NAE 1.15: 9657 seconds -> 24 seconds | Helped |
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