# Compressible Spectral Mixture Kernels with Sparse Dependency Structures for Gaussian Processes

arXiv: https://arxiv.org/abs/1808.00560 · HTML: https://mlsanity.com/paper/1808.00560/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Aug 2018.

## Built on by (most cited first, 2 of 2)

- [Domain Invariant Learning for Gaussian Processes and Bayesian Exploration](https://mlsanity.com/paper/2312.11318/) (2023)
- [Navigating Efficiency in MobileViT through Gaussian Process on Global Architecture Factors](https://mlsanity.com/paper/2406.04820/) (2024)

## Abstract (arXiv)

Spectral mixture (SM) kernels comprise a powerful class of generalized kernels for Gaussian processes (GPs) to describe complex patterns. This paper introduces model compression and time- and phase (TP) modulated dependency structures to the original (SM) kernel for improved generalization of GPs. Specifically, by adopting Bienaym'es identity, we generalize the dependency structure through cross-covariance between the SM components. Then, we propose a novel SM kernel with a dependency structure (SMD) by using cross-convolution between the SM components. Furthermore, we ameliorate the expressiveness of the dependency structure by parameterizing it with time and phase delays. The dependency structure has clear interpretations in terms of spectral density, covariance behavior, and sampling path. To enrich the SMD with effective hyperparameter initialization, compressible SM kernel components, and sparse dependency structures, we introduce a novel structure adaptation (SA) algorithm in the end. A thorough comparative analysis of the SMD on both synthetic and real-life applications corroborates its efficacy.