# Making Convex Loss Functions Robust to Outliers using $e$-Exponentiated Transformation

## TL;DR

This paper introduces an $e$-exponentiated transformation to convex loss functions, enhancing robustness to outliers and label noise, with theoretical guarantees and empirical improvements over traditional methods.

## Contribution

It proposes a new $e$-exponentiated transformation for loss functions, providing theoretical bounds and demonstrating empirical robustness to outliers.

## Key findings

- Transformed loss functions are more robust to outliers.
- Theoretical bounds are tighter for datasets with outliers.
- Empirical results show improved accuracy under label noise.

## Abstract

In this paper, we propose a novel {\em $e$-exponentiated} transformation, $0 \le e<1$, for loss functions. When the transformation is applied to a convex loss function, the transformed loss function become more robust to outliers. Using a novel generalization error bound, we have theoretically shown that the transformed loss function has a tighter bound for datasets corrupted by outliers. Our empirical observation shows that the accuracy obtained using the transformed loss function can be significantly better than the same obtained using the original loss function and comparable to that obtained by some other state of the art methods in the presence of label noise.