# Learning Rates of Regression with q-norm Loss and Threshold

## TL;DR

This paper investigates robust regression methods using q-norm loss functions within reproducing kernel Hilbert spaces, providing theoretical error bounds and learning rates under noise conditions.

## Contribution

It introduces variance-expectation bounds for q-norm loss regression and derives explicit learning rates based on kernel approximation assumptions.

## Key findings

- Established variance-expectation bounds under noise conditions
- Derived explicit learning rates for q-norm loss regression
- Provided theoretical error bounds in RKHS setting

## Abstract

This paper studies some robust regression problems associated with the $q$-norm loss ($q\ge1$) and the $\epsilon$-insensitive $q$-norm loss in the reproducing kernel Hilbert space. We establish a variance-expectation bound under a priori noise condition on the conditional distribution, which is the key technique to measure the error bound. Explicit learning rates will be given under the approximation ability assumptions on the reproducing kernel Hilbert space.