# Improving the local scoring algorithm using gradient sampling

## TL;DR

This paper introduces an enhanced local scoring algorithm that employs gradient sampling to handle non-smooth optimization problems, improving stability and applicability to real-world data analysis tasks.

## Contribution

The authors adapt the gradient sampling technique to the local scoring algorithm, enabling it to effectively optimize non-differentiable objective functions.

## Key findings

- Improved numerical stability in local scoring algorithms.
- Successful application to quantile regression and peaks-over-threshold methods.
- Demonstrated effectiveness on retail and temperature datasets.

## Abstract

We adapt the gradient sampling algorithm to the local scoring algorithm to solve complex estimation problems based on an optimization of an objective function. This overcomes non-differentiability and non-smoothness of the objective function. The new algorithm estimates the Clarke generalized subgradient used in the local scoring, thus reducing numerical instabilities. The method is applied to quantile regression and to the peaks-over-threshold method, as two examples. Real applications are provided for a retail store and temperature data analysis.