# Regularized Multi-output Gaussian Convolution Process with Domain Adaptation

arXiv: https://arxiv.org/abs/2409.02778 · HTML: https://mlsanity.com/paper/2409.02778/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 45 references that are in the map.
- First posted on arXiv 4 Sep 2024.

## Builds on (most cited first, 7 of 7)

- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Convolutional Gaussian Processes](https://mlsanity.com/paper/1709.01894/) (2017)
- [Heterogeneous Multi-output Gaussian Process Prediction](https://mlsanity.com/paper/1805.07633/) (2018)
- [Scalable Exact Inference in Multi-Output Gaussian Processes](https://mlsanity.com/paper/1911.06287/) (2019)
- [Graph Convolutional Gaussian Processes](https://mlsanity.com/paper/1905.05739/) (2019)
- [Leveraging Probabilistic Circuits for Nonparametric Multi-Output Regression](https://mlsanity.com/paper/2106.08687/) (2021)
- [Minimizing Negative Transfer of Knowledge in Multivariate Gaussian Processes: A Scalable and Regularized Approach](https://mlsanity.com/paper/1901.11512/) (2019)

## Built on by (most cited first, 3 of 3)

- [Non-stationary and Sparsely-correlated Multi-output Gaussian Process with Spike-and-Slab Prior](https://mlsanity.com/paper/2409.03149/) (2024)
- [Local transfer learning Gaussian process modeling, with applications to surrogate modeling of expensive computer simulators](https://mlsanity.com/paper/2410.12690/) (2024)
- [R^2-HGP: A Double-Regularized Gaussian Process for Heterogeneous Transfer Learning](https://mlsanity.com/paper/2512.10258/) (2025)

## Abstract (arXiv)

Multi-output Gaussian process (MGP) has been attracting increasing attention as a transfer learning method to model multiple outputs. Despite its high flexibility and generality, MGP still faces two critical challenges when applied to transfer learning. The first one is negative transfer, which occurs when there exists no shared information among the outputs. The second challenge is the input domain inconsistency, which is commonly studied in transfer learning yet not explored in MGP. In this paper, we propose a regularized MGP modeling framework with domain adaptation to overcome these challenges. More specifically, a sparse covariance matrix of MGP is proposed by using convolution process, where penalization terms are added to adaptively select the most informative outputs for knowledge transfer. To deal with the domain inconsistency, a domain adaptation method is proposed by marginalizing inconsistent features and expanding missing features to align the input domains among different outputs. Statistical properties of the proposed method are provided to guarantee the performance practically and asymptotically. The proposed framework outperforms state-of-the-art benchmarks in comprehensive simulation studies and one real case study of a ceramic manufacturing process. The results demonstrate the effectiveness of our method in dealing with both the negative transfer and the domain inconsistency.