# Asymmetric kernel in Gaussian Processes for learning target variance

arXiv: https://arxiv.org/abs/1803.06952 · HTML: https://mlsanity.com/paper/1803.06952/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2018.

## Built on by (most cited first, 3 of 3)

- [Learning with Asymmetric Kernels: Least Squares and Feature Interpretation](https://mlsanity.com/paper/2202.01397/) (2022)
- [A Robust Asymmetric Kernel Function for Bayesian Optimization, with Application to Image Defect Detection in Manufacturing Systems](https://mlsanity.com/paper/2109.10898/) (2021)
- [Learning Analysis of Kernel Ridgeless Regression with Asymmetric Kernel Learning](https://mlsanity.com/paper/2406.01435/) (2024)

## Abstract (arXiv)

This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in the neighborhood of a certain sample through metric learning. We start by using data centers rather than all training samples. Subsequently, each center selects an individualized kernel metric. This enables each center to adjust the kernel space in its vicinity in correspondence with the topology of the targets --- a multi-modal approach. We additionally add descriptiveness by allowing each center to learn a precision matrix. We demonstrate empirically the reliability of the model.