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Logic-Logit: A Logic-Based Approach to Choice Modeling
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Proposes Logic-Logit, a rule-based mixed logit choice model whose utilities are OR-of-AND logic rules learned via Frank-Wolfe over preference types and column generation over rules, evaluated on synthetic, Expedia hotel and MIMIC-IV data.
Problem
Choice models based on neural networks are accurate but have many parameters and lack interpretability, while human consider-then-choose decisions often follow heuristic OR-of-AND rules that must be extracted from preference data, a NP-hard search.
Approach
Model each preference type's utility as a linear combination of conjunctive Boolean rule features, learn the mixture of preference types with a functional Frank-Wolfe algorithm, and find new rules with column generation using gradient-based scores and a risk-seeking quantile search.
Key results
- On synthetic data, 8 of 9 ground-truth rules were perfectly recovered (Jaccard 1).
- On Expedia (30 rules per type), Ours-RS-30 reached test top-1 accuracy 0.1738 versus 0.1489 for the best NN baseline (RUMNet) and 0.1657 for Mix-MNL.
- On MIMIC-IV, Ours-RS-50 reached test top-1 accuracy 0.26 versus 0.1000 for RUMNet, with extracted rules consistent with medical knowledge.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use risk-seeking mode instead of normal mode with 5 rules (ablation) | Logic-Logit · Synthetic | test accuracy (Top1): 0.2048(±0.011) -> 0.2058(±0.011) | Helped |
| Use risk-seeking mode instead of normal mode with 20 rules (ablation) | Logic-Logit · Synthetic | test accuracy (Top1): 0.1876(±0.007) -> 0.1908(±0.0064) | Helped |
| Increase the maximum rule number from 5 to 20 (ablation) | Logic-Logit · Synthetic | test accuracy (Top1): 0.2048(±0.011) -> 0.1876(±0.007) | Hurt |
| Use risk-seeking mode instead of normal mode (ablation) | Logic-Logit · Expedia Hotel | test accuracy (Top1): 0.1698(±0.009) -> 0.1738(±0.005) | Helped |
| Use risk-seeking mode instead of normal mode (ablation) | Logic-Logit · MIMIC-IV | test accuracy (Top1): 0.264(\pm0.029) -> 0.26(\pm0.016) | No clear effect |
Surprising findings
- The risk-seeking search was ineffective on the Expedia hotel dataset due to the dominance of the PageRank effect.
- Neural network baselines performed poorly on MIMIC-IV because the features are mainly patient-level rather than drug-level.
Limitations
- Predicates are predefined by percentile thresholding and fixed, so rule quality depends on predicate design.
- Rule search is limited to a maximum conjunction length and relies on heuristic BFS/DFS and random sampling.
- Reported accuracies on real data are low in absolute terms (around 0.17 to 0.26 top-1).
Experimental setup
Datasets: Synthetic choice data Expedia Hotel dataset MIMIC-IV
Benchmarks: Synthetic choice dataset Expedia Hotel dataset MIMIC-IV treatment choice
Metrics: negative log-likelihood top-1 accuracy Jaccard index
Baselines: MNL Mix-MNL Vanilla NN TasteNet DeepMNL Mix-DeepMNL RUMNet
Builds on: Mixed logit Frank-Wolfe algorithm Column generation Generalized Linear Rule Models RUMNet
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