# Sparsity-Aware Distributed Learning for Gaussian Processes with Linear Multiple Kernel

arXiv: https://arxiv.org/abs/2309.08201 · HTML: https://mlsanity.com/paper/2309.08201/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 62 references that are in the map.
- First posted on arXiv 15 Sep 2023.

## Builds on (most cited first, 20 of 20)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems](https://mlsanity.com/paper/1410.1390/) (2014)
- [Federated Learning With Quantized Global Model Updates](https://mlsanity.com/paper/2006.10672/) (2020)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [Rethinking Bayesian Learning for Data Analysis: The Art of Prior and Inference in Sparsity-Aware Modeling](https://mlsanity.com/paper/2205.14283/) (2022)
- [Linear Multiple Low-Rank Kernel Based Stationary Gaussian Processes Regression for Time Series](https://mlsanity.com/paper/1904.09559/) (2019)
- [Distributed Online Learning with Multiple Kernels](https://mlsanity.com/paper/2102.12733/) (2021)
- [ADMM Penalty Parameter Selection by Residual Balancing](https://mlsanity.com/paper/1704.06209/) (2017)
- [Probabilistic Attention based on Gaussian Processes for Deep Multiple Instance Learning](https://mlsanity.com/paper/2302.04061/) (2023)
- [Parallel and Distributed Successive Convex Approximation Methods for Big-Data Optimization](https://mlsanity.com/paper/1805.06963/) (2018)
- [Large-scale Heteroscedastic Regression via Gaussian Process](https://mlsanity.com/paper/1811.01179/) (2018)
- [Wireless Traffic Prediction with Scalable Gaussian Process: Framework, Algorithms, and Verification](https://mlsanity.com/paper/1902.04763/) (2019)
- [Quantized Consensus by the ADMM: Probabilistic versus Deterministic Quantizers](https://mlsanity.com/paper/1502.01053/) (2015)
- [Quantized Consensus ADMM for Multi-Agent Distributed Optimization](https://mlsanity.com/paper/1510.08736/) (2015)
- [Recent Advances in Data-Driven Wireless Communication Using Gaussian Processes: A Comprehensive Survey](https://mlsanity.com/paper/2103.10134/) (2021)

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

- [Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2503.18309/) (2025)
- [Robust Bayesian Optimization with Q-Exponential Surrogates](https://mlsanity.com/paper/2609.32775/) (2026)

## Abstract (arXiv)

Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyper-parameter optimization. This paper presents a novel GP linear multiple kernel (LMK) and a generic sparsity-aware distributed learning framework to optimize the hyper-parameters. The newly proposed grid spectral mixture product (GSMP) kernel is tailored for multi-dimensional data, effectively reducing the number of hyper-parameters while maintaining good approximation capability. We further demonstrate that the associated hyper-parameter optimization of this kernel yields sparse solutions. To exploit the inherent sparsity of the solutions, we introduce the Sparse LInear Multiple Kernel Learning (SLIM-KL) framework. The framework incorporates a quantized alternating direction method of multipliers (ADMM) scheme for collaborative learning among multiple agents, where the local optimization problem is solved using a distributed successive convex approximation (DSCA) algorithm. SLIM-KL effectively manages large-scale hyper-parameter optimization for the proposed kernel, simultaneously ensuring data privacy and minimizing communication costs. Theoretical analysis establishes convergence guarantees for the learning framework, while experiments on diverse datasets demonstrate the superior prediction performance and efficiency of our proposed methods.