Hierarchical Gaussian Processes with Wasserstein-2 Kernels
This addresses outlier detection issues in hierarchical Gaussian Processes for machine learning applications, but appears incremental as it builds on existing methods with specific modifications.
The paper tackled the problem of stacking Gaussian Processes diminishing outlier detection by proposing a hybrid kernel from Varifold theory that operates in Euclidean and Wasserstein space, showing improved performance on medium and large datasets and enhanced out-of-distribution detection on toy and real data.
Stacking Gaussian Processes severely diminishes the model's ability to detect outliers, which when combined with non-zero mean functions, further extrapolates low non-parametric variance to low training data density regions. We propose a hybrid kernel inspired from Varifold theory, operating in both Euclidean and Wasserstein space. We posit that directly taking into account the variance in the computation of Wasserstein-2 distances is of key importance towards maintaining outlier status throughout the hierarchy. We show improved performance on medium and large scale datasets and enhanced out-of-distribution detection on both toy and real data.