Regularized Multi-output Gaussian Convolution Process with Domain Adaptation (2409.02778v1)

Abstract: 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.

• The paper presents a novel approach that extends Gaussian Processes to multi-output tasks using a convolution framework and regularization to mitigate negative transfer.
• It introduces a domain adaptation strategy via marginalization and expansion, aligning different input domains to enhance transfer learning efficacy.
• The framework shows reduced computational complexity and robust performance in both simulated and real-world settings such as ceramic manufacturing.

Regularized Multi-output Gaussian Convolution Process with Domain Adaptation

Introduction

The paper "Regularized Multi-output Gaussian Convolution Process with Domain Adaptation" introduces an advanced framework for Multi-output Gaussian Process (MGP) focusing on overcoming challenges such as negative transfer and domain inconsistency that are prevalent in transfer learning scenarios. The authors propose a regularization-based approach within a Gaussian Convolution Process (GCP) to address these issues effectively, making significant contributions to both theoretical foundations and practical applications.

Framework and Methodology

Multi-output Gaussian Process

The authors extend the conventional Gaussian Process (GP), which traditionally deals with single-output tasks, to handle multiple outputs by modeling them jointly. They utilize a convolution process to construct a non-separable covariance function. This model not only maintains the desirable properties of GP, such as providing uncertainty quantification alongside predictions but also allows for the modeling of correlations across multiple outputs.

Regularization and Domain Adaptation

To combat negative transfer, where irrelevant source tasks might degrade the performance on the target task, a regularization framework is employed. This involves using a sparse covariance structure where regularization terms selectively include only the most informative outputs for knowledge transfer.

For handling domain inconsistency, where input domains differ across tasks, the authors propose a domain adaptation method by marginalization and expansion. This approach aligns the input domains among different outputs by transforming data into a feature space that facilitates effective domain adaptation without succumbing to negative transfer.

Theoretical Insights

The paper provides asymptotic properties and statistical guarantees for the proposed framework, ensuring that the regularized estimator identifies the true model with increasing data. The authors detailed the consistency and sparsity of the estimator under their framework, offering evidence that their regularization method can successfully discern between informative and non-informative source outputs in practical scenarios.

Implementation Considerations

The proposed MGCP is implemented with Gaussian kernels, and its regularization is achieved through methods such as $L_1$ norm. Optimizations utilize smooth approximations to handle non-differentiability issues common in regularization problems.

Complexity and Scalability

The computational complexity of the framework is significantly reduced compared to full covariance models due to its sparsity. The complexity is approximately $O(qn^3 + n_t^3)$, where $q$ is the number of source outputs and $n$ and $n_t$ are the number of data points in sources and target, respectively.

Experimental Evaluation

The framework demonstrated superior performance in simulation studies and a real-world ceramic manufacturing case. Key takeaways include:

• Reduction of Negative Transfer: Demonstrated by excluding irrelevant sources in simulated settings, thereby improving predictive accuracy.
• Domain Adaptation Effectiveness: Successfully aligned inconsistent input domains, facilitating better transfer learning in complex scenarios such as ceramic density prediction based on diverse manufacturing techniques.
• Scalability: The framework maintained efficiency and efficacy with increasing dimensions and source numbers, highlighted in extended simulation results.

Conclusion

The developed regularized MGCP framework with robust domain adaptation strategies represents a substantial advancement in multi-task learning, particularly for real-world applications plagued by domain incongruities and negative transfer. Future research directions proposed by the authors include the extension of this framework to classification problems, dealing with correlated noise, and a more integrated approach to modeling and domain adaptation. Overall, the paper contributes a comprehensive methodological innovation poised to enhance the utility and flexibility of MGP in complex problem settings.