Asymmetric kernel in Gaussian Processes for learning target variance
This is an incremental improvement for Gaussian Process regression in handling multi-modal data distributions.
The authors tackled the problem of incorporating data multi-modality into Gaussian Process regression by learning target space variance through metric learning, using data centers with individualized kernel metrics and precision matrices, and demonstrated empirical reliability.
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.