Gaussian Mixture Regression Model with Sparsity for Clustering of Territory Risk in Auto Insurance
Bibliographic record
Abstract
Abstract Insurance rating territory design and accurate estimation of territory risk relativities are fundamental aspects of auto insurance rate regulation. It is crucial to develop methodologies that can facilitate the effective design of rating territories and their risk relativities estimate, as they directly impact the rate filing and the decision support of the rate change review process. This article proposes a Gaussian Mixture Regression model clustering approach for territory design. The proposed method incorporates a linear regression model, taking spatial location as model covariates, which helps estimate the cluster mean more accurately. Also, to further enhance the estimation of territory risk relativities, we impose sparsity through sparse matrix decomposition of the membership coefficient matrix obtained from the Gaussian Mixture Regression model. By transitioning from the current hard clustering method to a soft approach, our methodology could improve the evaluation of territory risk for rate-making purposes. Moreover, using non-negative sparse matrix approximation ensures that the estimation of risk relativities for basic rating units remains smooth, effectively eliminating data noise from the territory risk relativity estimate. Overall, our novel methodology aims to significantly enhance the accuracy and reliability of risk analysis in auto insurance. Furthermore, the proposed method exhibits potential for extension to various other domains that involve spatial clustering of data, thereby broadening its applicability and expanding its usefulness beyond auto insurance rate regulation.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".