# Distribution-free inference for LightGBM and GLM with Tweedie loss

arXiv: https://arxiv.org/abs/2507.06921 · HTML: https://mlsanity.com/paper/2507.06921/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 44 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Builds on (most cited first, 8 of 8)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Insurance Premium Prediction via Gradient Tree-Boosted Tweedie Compound Poisson Models](https://mlsanity.com/paper/1508.06378/) (2015)
- [Enhanced Gradient Boosting for Zero-Inflated Insurance Claims and Comparative Analysis of CatBoost, XGBoost, and LightGBM](https://mlsanity.com/paper/2307.07771/) (2023)
- [Extended Poisson-Tweedie: properties and regression models for count data](https://mlsanity.com/paper/1608.06888/) (2016)
- [Some Clustering-based Change-point Detection Methods Applicable to High Dimension, Low Sample Size Data](https://mlsanity.com/paper/2111.14012/) (2021)
- [Spatial Tweedie exponential dispersion models](https://mlsanity.com/paper/2003.06299/) (2020)
- [Bayesian Variable Selection in Double Generalized Linear Tweedie Spatial Process Models](https://mlsanity.com/paper/2306.11165/) (2023)
- [Interval Estimation of Coefficients in Penalized Regression Models of Insurance Data](https://mlsanity.com/paper/2410.01008/) (2024)

## Built on by (most cited first, 1 of 1)

- [Bayesian Models for Joint Selection of Features and Auto-Regressive Lags: Theory and Applications in Environmental and Financial Forecasting](https://mlsanity.com/paper/2508.10055/) (2025)

## Abstract (arXiv)

Prediction uncertainty quantification is a key research topic in recent years scientific and business problems. In insurance industries (citeparodi2023pricing), assessing the range of possible claim costs for individual drivers improves premium pricing accuracy. It also enables insurers to manage risk more effectively by accounting for uncertainty in accident likelihood and severity. In the presence of covariates, a variety of regression-type models are often used for modeling insurance claims, ranging from relatively simple generalized linear models (GLMs) to regularized GLMs to gradient boosting models (GBMs). Conformal predictive inference has arisen as a popular distribution-free approach for quantifying predictive uncertainty under relatively weak assumptions of exchangeability, and has been well studied under the classic linear regression setting. In this work, we propose new non-conformity measures for GLMs and GBMs with GLM-type loss. Using regularized Tweedie GLM regression and LightGBM with Tweedie loss, we demonstrate conformal prediction performance with these non-conformity measures in insurance claims data. Our simulation results favor the use of locally weighted Pearson residuals for LightGBM over other methods considered, as the resulting intervals maintained the nominal coverage with the smallest average width.