Research map / Learning theory and algorithms / Sample complexity
Optimal Scaling for Locally Balanced Proposals in Discrete Spaces
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Adapt the update scale instead of fixing it at one site | LBP · Bernoulli | EJD: 1.00 -> 78.63 | Helped |
| Adapt the update scale instead of fixing it at one site | LBP · Ising | EJD: 1.00 -> 96.23 | Helped |
| Adapt the update scale instead of fixing it at one site | LBP · FHMM | EJD: 1.00 -> 242.01 | Helped |
| Adapt the update scale instead of fixing it at one site | LBP · RBM | EJD: 0.98 -> 26.07 | Helped |
| Adapt the update scale rather than fix the proposal to one flip | RWM · Bernoulli, Ising, FHMM | EJD: 0.65 -> 1.70; 0.64 -> 1.58; 0.79 -> 4.32 | Helped |
| Adapt the update scale rather than fix the proposal to one flip | RWM · RBM | EJD: 0.17 -> 0.17 | No clear effect |
| Use adaptive scaling rather than grid-search scaling | LBP · Bernoulli, Ising, FHMM, RBM | EJD: 78.63 vs 78.83; 96.23 vs 96.68; 242.01 vs 242.52; 26.07 vs 25.86 | Mixed |
| Adapt the scale for PCD sampling | LBP_b · Static MNIST | minimum M-H steps for PCD: 90 -> 20 | Helped |
| Adapt the scale for PCD sampling | LBP_s · Omniglot | minimum M-H steps for PCD: 30 -> 5 | Helped |
| Use LBP with scale R proportional to N^(2/3), tuned to acceptance rate 0.574 | LBP · Discrete product targets | expected jump distance: 0.574 | Helped |
| Use RWM with its optimal acceptance rate 0.234 rather than a larger update scale | RWM · Discrete product targets | expected jump distance: 0.234 | Helped |
| Use optimally scaled LBP instead of optimally scaled RWM | LBP versus RWM · Discrete models as dimension N grows | relative efficiency: O(N^(2/3)) | Helped |
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