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Learning GAI-Decomposable Utility Models for Multiattribute Decision Making
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Learns a sparse GAI-decomposable multiattribute utility model from preference examples by combining zero-integral (ANOVA) kernels with L1-regularized multiple kernel learning, without restricting interaction size.
Problem
Learning multiattribute utility functions that capture interacting attributes while keeping the model as simple and decomposable as possible, including identifying the interaction factors (structure) and their sub-utilities for continuous or discrete attributes.
Approach
Uses multiple kernel learning with an L1 penalty on kernel weights over a product-kernel basis for all attribute subsets, with zero-integral univariate kernels so the learned model is a unique ANOVA decomposition; the sparse ANOVA factors are then aggregated into a well-formed GAI decomposition.
Key results
- On the ERA dataset, SMKGAI achieves MAE 0.04749 ± 0.00200 versus 0.11817 for 2-GAI and 0.24255 for linear regression.
- On synthetic high-interaction data (n=6), SMKGAI reduces MAE to 0.0065 compared to 0.0381 for 1-GAI, at roughly twice the training time of the additive model.
- On ESL, linear regression (0.08198) and 1-GAI (0.08266) perform best, so SMKGAI is not uniformly superior; the false discovery rate stays below 20% in model recovery experiments.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use sparse multiple-kernel GAI learning instead of 2-GAI | Utility learning · LEV | MAE: 0.17093 ± 0.01212 -> 0.12381 ± 0.02662 | Helped |
| Use sparse multiple-kernel GAI learning instead of 2-GAI | Utility learning · ERA | MAE: 0.11817 ± 0.00932 -> 0.04749 ± 0.00200 | Helped |
| Use sparse multiple-kernel GAI learning instead of 1-GAI | Utility learning · ESL | MAE: 0.08266 ± 0.00619 -> 0.08419 ± 0.00697 | No clear effect |
| Use sparse multiple-kernel GAI learning instead of 2-GAI | Utility learning · CPU | MAE: 0.00796 ± 0.00475 -> 0.00805 ± 0.00455 | No clear effect |
| Use sparse multiple-kernel GAI learning instead of 2-GAI | Utility learning · MPG | MAE: 0.05355 ± 0.00656 -> 0.05212 ± 0.00666 | Helped |
| Use sparse multiple-kernel GAI learning instead of 1-GAI | Utility learning · CITY | MAE: 0.04855 ± 0.00916 -> 0.05054 ± 0.00893 | No clear effect |
| Allow sparse high-order interactions rather than restricting the model to 1-GAI | Synthetic product model · Synthetic product model | MAE: 0.0381 ± 0.0088 -> 0.0065 ± 0.0016 | Helped |
| Allow sparse high-order interactions rather than restricting the model to 1-GAI | Synthetic product model · Synthetic product model | Training time: 34.89 ± 2.35 -> 75.48 ± 6.78 | Hurt |
Surprising findings
- On the ESL dataset, the simple linear regression and additive 1-GAI models outperform the proposed SMKGAI method.
Limitations
- Number of possible factors grows exponentially with the number of attributes, limiting scalability.
- Recovery of factors degrades with higher interaction degree, with false inclusions up to about 20%.
- Does not outperform simple baselines on all datasets (e.g., ESL).
Experimental setup
Datasets: ESL LEV ERA CPU MPG CITY synthetic data generated from B-spline GAI models
Benchmarks: ESL LEV ERA CPU MPG CITY synthetic GAI utility models
Metrics: mean absolute error training time false discovery rate
Baselines: linear regression 2-additive Choquet integral 1-GAI 2-GAI 3-GAI 4-GAI
Builds on: support vector regression multiple kernel learning ANOVA decomposition GAI decomposition zero-integral kernels (Durrande et al. 2013)
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