# Asymmetric kernel in Gaussian Processes for learning target variance

## TL;DR

This paper introduces a Gaussian Process model that learns local target variances using multi-modal data and individualized kernels, improving adaptability to complex data distributions.

## Contribution

It proposes a novel multi-modal Gaussian Process regression with individualized kernels and learned target space variance, enhancing modeling flexibility.

## Key findings

- Model effectively captures multi-modal data distributions.
- Empirical results demonstrate improved prediction accuracy.
- Kernel customization per data center enhances local modeling.

## Abstract

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.