A Nested GLM Framework with Neural Network Encoding and Spatially Constrained Clustering in Non-Life Insurance Ratemaking
Bibliographic record
Abstract
The generalized linear model (GLM) is a popular modeling choice for pricing non-life insurance policies. However, high-cardinality categorical insurance data presents significant challenges for these GLM rate-making models. Additionally, insurance regulators often require rating territories, which are clusters of insurance policies’ geographic locations for setting insurance rates, to meet certain standards. For instance, (1) the credibility standard ensures that the number of policies in a territory is large enough to be credible and representative, (2) the contiguity standard requires the locations in each territory to be geographically adjacent to promote a logical and practical spatial grouping, and (3) the cardinality standard specifies an acceptable range for the number of territories in a geographic area. To address these challenges, this article proposes a nested GLM framework for non-life insurance rate-making applications. In this framework, neural network models with categorical embedding layers are constructed to model the residual deviance from simple GLMs, using high-cardinality categorical variables as input. Low-dimensionly features extracted from the neural network model effectively translate categorical variables into meaningful numerical representations, capturing their effects on the initial model’s residuals. The features corresponding to the location-related variable are further converted into a contiguous territory rating variable via spatially constrained clustering models. By incorporating outcomes from these models, the nested GLM not only satisfies regulatory requirements but also enhances the model’s predictive power, while maintaining the interpretability from the (generalized) linear form. The construction of a nested Poisson GLM is presented in this article. Its performance is demonstrated using a real-life Brazil auto insurance data to model claim frequency.
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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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".