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Generating Origin-Destination Matrices in Neural Spatial Interaction Models
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Proposes GeNSIT, a framework that jointly samples discrete origin-destination matrices under summary-statistic constraints (via Gibbs Markov basis sampling) while neurally calibrating Harris-Wilson-driven spatial interaction model parameters, scaling linearly in the number of OD pairs.
Problem
Generating discrete origin-destination matrices for agent-based models subject to partially observed summary statistics; existing methods work on continuous intensity relaxations with discretisation errors, or are computationally expensive MCMC.
Approach
Combine a neural-network-calibrated Spatial Interaction Model coupled with the Harris-Wilson SDE (solved by Euler-Maruyama) with closed-form or Gibbs Markov basis sampling of the discrete contingency table, with a Joint scheme passing table information into the NN loss, giving linear-in-IJ cost.
Key results
- On Cambridge, GeNSIT Joint reaches SRMSE 0.43 and 93% CP for singly constrained table vs SIM-MCMC/SIM-NN comparisons in Table 1 (intensity-level baselines).
- On Washington DC, GeNSIT Joint achieves SRMSE 2.37±0.08 and 44% CP in table space, outperforming GMEL and SIM-NN on reconstruction error and coverage.
- Claimed speed-up of O(J^2) over SIM-MCMC and SIT-MCMC; GeNSIT scales linearly in IJ.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GeNSIT Joint instead of SIM-MCMC | Cambridge ODM, total constrained · Cambridge ODM, total constrained | SRMSE: 0.70 -> 2.43 | Hurt |
| Use GeNSIT Joint instead of SIM-MCMC | Cambridge ODM, total constrained · Cambridge ODM, total constrained | 99% CP: 68% -> 31% | Hurt |
| Use GeNSIT Joint instead of SIT-MCMC | Cambridge ODM, singly constrained · Cambridge ODM, singly constrained | SRMSE: 0.61 -> 0.43 | Helped |
| Use GeNSIT Joint instead of SIT-MCMC | Cambridge ODM, singly constrained · Cambridge ODM, singly constrained | 99% CP: 72% -> 93% | Helped |
| Use GeNSIT Joint instead of SIT-MCMC | Cambridge ODM, doubly constrained · Cambridge ODM, doubly constrained | SRMSE: 0.59 -> 0.55 | Hurt |
| Use GeNSIT Joint instead of SIT-MCMC | Cambridge ODM, doubly constrained · Cambridge ODM, doubly constrained | 99% CP: 86% -> 89% | Helped |
| Fix 10% of cells in addition to row and column margins (ablation) | GeNSIT Joint · Cambridge ODM, doubly constrained with 10% cells fixed | SRMSE: 0.55 -> 0.43 | Helped |
| Fix 20% of cells in addition to row and column margins (ablation) | GeNSIT Joint · Cambridge ODM, doubly constrained with 20% cells fixed | SRMSE: 0.55 -> 0.38 | Helped |
| Pass table information to the loss (Joint rather than Disjoint) (ablation) | GeNSIT, Washington ODM · Washington ODM, total and training-cell constrained | SRMSE: 2.39±0.09 -> 2.37±0.08 | Helped |
| Pass table information to the loss (Joint rather than Disjoint) (ablation) | GeNSIT, Washington ODM · Washington ODM, total and training-cell constrained | 99% CP: 47%±1% -> 44%±1% | Hurt |
| Use GeNSIT table estimates rather than continuous SIM-NN estimates | Washington ODM · Washington ODM, total and training-cell constrained | SRMSE: 2.47±0.00 -> 2.37±0.08 | Helped |
| Use GeNSIT table estimates rather than continuous GMEL estimates | Washington ODM · Washington ODM, total and training-cell constrained | 99% CP: 5%± 1% -> 44%±1% | Helped |
Surprising findings
- SIT-MCMC outperforms GeNSIT in the totally constrained Cambridge case, attributed to its theta support restriction to [0,2]^2 acting as regularisation.
- Disjoint scheme does not propagate table constraint information to intensity updates, yielding no SRMSE or CP improvement over iterations.
Limitations
- Spatial interaction model assumes a specific utility/entropy-based decision process, which may not capture irregular trip data.
- Incorporating additional structural constraints (e.g. symmetry, sparsity) is left as open; the tractable closed-form sampling only applies to at most one marginal.
- Doubly constrained sampling relies on MCMC with computational overhead; Washington comparisons with MCMC baselines were infeasible.
Experimental setup
Datasets: Cambridge UK census ODM (ONS population census) Washington DC commuting ODM
Benchmarks: Cambridge UK ODM Washington DC ODM synthetic ODM scalability
Metrics: SRMSE 99% coverage probability (CP) SSI computation time
Baselines: SIM-MCMC SIM-NN SIT-MCMC GMEL
Builds on: Harris-Wilson SDE spatial interaction models Markov basis MCMC (Diaconis-Sturmfels) SIM-NN
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