Research map / Probabilistic and scientific modeling / Variational and generative sampling
Learning Markov Random Fields for Combinatorial Structures via Sampling through Lovász Local Lemma
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LLL-based resampling in contrastive-divergence learning instead of Gibbs sampling | Constrained MRF learning on random K-SAT · Random K-SAT, problem size 1000 | training time per iteration (Mins): 854.59 -> 34.01 | Helped |
| Use LLL-based resampling rather than QuickSampler | Constrained MRF learning on random K-SAT · Random K-SAT, problem size 1000 | validness (%): 0.00 -> 100 | Helped |
| Use LLL-based resampling rather than Gibbs sampling | Constrained MRF learning on random K-SAT · Random K-SAT, problem size 1000 | validness (%): 33.91 -> 100 | Helped |
| Use LLL-based resampling rather than Gibbs sampling | Constrained MRF learning on random K-SAT · Random K-SAT, problem size 18 | approximation error of ∇log Z_C(θ): 1.90 -> 0.18 | Helped |
| Use Nelson-CD rather than Gibbs-based CD | Constrained MRF learning on random K-SAT solutions with preferences · Random K-SAT, problem size 1000 | log-likelihood: -296.33 -> -294.22 | Helped |
| Use Nelson-CD rather than Gibbs-based CD | Constrained MRF learning on random K-SAT solutions with preferences · Random K-SAT, problem size 1000 | MAP@10 (%): 77.56 -> 91.70 | Helped |
| Use LLL-based resampling rather than CMSGen | Constrained MRF learning on sink-free orientations · Sink-free orientations, problem size 50 | training time per epoch (Mins): 9.08 -> 1.17 | Helped |
| Use LLL-based resampling rather than Gibbs sampling | Constrained MRF learning on sink-free orientations · Sink-free orientations, problem size 11 | validness (%): 84.95 -> 100 | Helped |
| Use LLL-based resampling rather than Gibbs sampling | Constrained MRF learning on sink-free orientations · Sink-free orientations, problem size 13 | approximation error of ∇log Z_C(θ): 0.28 -> 0.05 | Helped |
| Use Nelson-CD rather than CMSGen-based learning | Constrained MRF learning on sink-free orientations · Sink-free orientations, problem size 50 | MAP@10 (%): 42.11 -> 46.12 | Helped |
| Apply Nelson sampling to vehicle delivery routes whose constraints do not satisfy the extremal condition | Vehicle delivery routes · TSPLIB Bavaria, 29 cities | resamples per batch: roughly 50 | Mixed |
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