# Non-stationary and Sparsely-correlated Multi-output Gaussian Process with Spike-and-Slab Prior

arXiv: https://arxiv.org/abs/2409.03149 · HTML: https://mlsanity.com/paper/2409.03149/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 72 references that are in the map.
- First posted on arXiv 5 Sep 2024.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Transfer Learning in Deep Reinforcement Learning: A Survey](https://mlsanity.com/paper/2009.07888/) (2020)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Multi-Task Reinforcement Learning with Soft Modularization](https://mlsanity.com/paper/2003.13661/) (2020)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Memory In Memory: A Predictive Neural Network for Learning Higher-Order Non-Stationarity from Spatiotemporal Dynamics](https://mlsanity.com/paper/1811.07490/) (2018)
- [Non-Stationary Gaussian Process Regression with Hamiltonian Monte Carlo](https://mlsanity.com/paper/1508.04319/) (2015)
- [DSTP-RNN: a dual-stage two-phase attention-based recurrent neural networks for long-term and multivariate time series prediction](https://mlsanity.com/paper/1904.07464/) (2019)
- [Spatial Mapping with Gaussian Processes and Nonstationary Fourier Features](https://mlsanity.com/paper/1711.05615/) (2017)
- [Partitioned Active Learning for Heterogeneous Systems](https://mlsanity.com/paper/2105.08547/) (2021)
- [Dynamic Multivariate Functional Data Modeling via Sparse Subspace Learning](https://mlsanity.com/paper/1804.03797/) (2018)
- [Multi-Output Gaussian Processes for Crowdsourced Traffic Data Imputation](https://mlsanity.com/paper/1812.08739/) (2018)
- [Fast and Scalable Spike and Slab Variable Selection in High-Dimensional Gaussian Processes](https://mlsanity.com/paper/2111.04558/) (2021)
- [Nonstationary Multivariate Gaussian Processes for Electronic Health Records](https://mlsanity.com/paper/1910.05851/) (2019)
- [Joint Spatio-Temporal Precoding for Practical Non-Stationary Wireless Channels](https://mlsanity.com/paper/2211.06017/) (2022)
- [Fleet Control using Coregionalized Gaussian Process Policy Iteration](https://mlsanity.com/paper/1911.10121/) (2019)
- [Learning Non-Stationary Space-Time Models for Environmental Monitoring](https://mlsanity.com/paper/1804.10535/) (2018)
- [Regularized Multi-output Gaussian Convolution Process with Domain Adaptation](https://mlsanity.com/paper/2409.02778/) (2024)
- [Dynamic Variable Selection with Spike-and-Slab Process Priors](https://mlsanity.com/paper/1708.00085/) (2017)
- [Online Structural Change-point Detection of High-dimensional Streaming Data via Dynamic Sparse Subspace Learning](https://mlsanity.com/paper/2009.11713/) (2020)
- [Hybrid Modeling of Regional COVID-19 Transmission Dynamics in the U.S](https://mlsanity.com/paper/2112.10983/) (2021)

## Built on by (most cited first, 1 of 1)

- [Residual Correlation as a Diagnostic for Joint-Uncertainty Gains from GP Coregionalisation](https://mlsanity.com/paper/2609.30085/) (2026)

## Abstract (arXiv)

Multi-output Gaussian process (MGP) is commonly used as a transfer learning method to leverage information among multiple outputs. A key advantage of MGP is providing uncertainty quantification for prediction, which is highly important for subsequent decision-making tasks. However, traditional MGP may not be sufficiently flexible to handle multivariate data with dynamic characteristics, particularly when dealing with complex temporal correlations. Additionally, since some outputs may lack correlation, transferring information among them may lead to negative transfer. To address these issues, this study proposes a non-stationary MGP model that can capture both the dynamic and sparse correlation among outputs. Specifically, the covariance functions of MGP are constructed using convolutions of time-varying kernel functions. Then a dynamic spike-and-slab prior is placed on correlation parameters to automatically decide which sources are informative to the target output in the training process. An expectation-maximization (EM) algorithm is proposed for efficient model fitting. Both numerical studies and a real case demonstrate its efficacy in capturing dynamic and sparse correlation structure and mitigating negative transfer for high-dimensional time-series data. Finally, a mountain-car reinforcement learning case highlights its potential application in decision making problems.