# On the Connection between Lp and Risk Consistency and its Implications on Regularized Kernel Methods

arXiv: https://arxiv.org/abs/2303.15210 · HTML: https://mlsanity.com/paper/2303.15210/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 47 references that are in the map.
- First posted on arXiv 27 Mar 2023.

## Builds on (most cited first, 5 of 5)

- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Universal Consistency of Deep Convolutional Neural Networks](https://mlsanity.com/paper/2106.12498/) (2021)
- [Learning Rates for Kernel-Based Expectile Regression](https://mlsanity.com/paper/1702.07552/) (2017)
- [Total Stability of SVMs and Localized SVMs](https://mlsanity.com/paper/2101.12678/) (2021)
- [Dimensionality Reduction and Wasserstein Stability for Kernel Regression](https://mlsanity.com/paper/2203.09347/) (2022)

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

- [Lp- and Risk Consistency of Localized SVMs](https://mlsanity.com/paper/2305.09385/) (2023)

## Abstract (arXiv)

As a predictor's quality is often assessed by means of its risk, it is natural to regard risk consistency as a desirable property of learning methods, and many such methods have indeed been shown to be risk consistent. The first aim of this paper is to establish the close connection between risk consistency and Lp-consistency for a considerably wider class of loss functions than has been done before. The attempt to transfer this connection to shifted loss functions surprisingly reveals that this shift does not reduce the assumptions needed on the underlying probability measure to the same extent as it does for many other results. The results are applied to regularized kernel methods such as support vector machines.