Optimal Bayesian Transfer Learning (1801.00857v2)

Abstract: Transfer learning has recently attracted significant research attention, as it simultaneously learns from different source domains, which have plenty of labeled data, and transfers the relevant knowledge to the target domain with limited labeled data to improve the prediction performance. We propose a Bayesian transfer learning framework where the source and target domains are related through the joint prior density of the model parameters. The modeling of joint prior densities enables better understanding of the "transferability" between domains. We define a joint Wishart density for the precision matrices of the Gaussian feature-label distributions in the source and target domains to act like a bridge that transfers the useful information of the source domain to help classification in the target domain by improving the target posteriors. Using several theorems in multivariate statistics, the posteriors and posterior predictive densities are derived in closed forms with hypergeometric functions of matrix argument, leading to our novel closed-form and fast Optimal Bayesian Transfer Learning (OBTL) classifier. Experimental results on both synthetic and real-world benchmark data confirm the superb performance of the OBTL compared to the other state-of-the-art transfer learning and domain adaptation methods.

• The paper introduces a novel Bayesian framework that derives closed-form posterior solutions to transfer statistical insights from source to target domains.
• The method significantly outperforms existing algorithms on synthetic and real datasets by optimizing classification accuracy.
• The framework employs a Laplace approximation for scalable computation and shows robustness against variations in key hyperparameter settings.

An Overview of "Optimal Bayesian Transfer Learning"

The paper "Optimal Bayesian Transfer Learning" proposes an innovative Bayesian framework designed to enhance traditional transfer learning methodologies. Transfer learning is a powerful approach that leverages a plethora of labeled data from source domains to improve prediction performance in a target domain where labeled data is scarce. This paper addresses the homogeneous transfer learning scenario, in which both source and target domains share the same feature space dimension, establishing a connection via joint prior density of model parameters.

The authors introduce a novel method termed Optimal Bayesian Transfer Learning (OBTL), which is an extension of the Optimal Bayesian Classifier (OBC) principles. The framework utilizes the joint Wishart distribution for precision matrices, enabling the transfer of pertinent statistical knowledge from source to target domains. Consequently, the contributions comprise the derivation of closed-form posterior distributions and posterior predictive densities, which inherently optimize the OBTL classifier through hypergeometric functions of matrix argument.

Key Contributions and Findings

1. Theoretical Development: The work is grounded on a rigorous Bayesian perspective that formulates closed-form solutions. It employs a joint Gaussian-Wishart prior distribution for the precision matrices between domains, extending the closed-form solutions integral to the Bayesian framework.
2. Superiority Over Existing Methods: Experimental validation underscores the superiority of OBTL compared to state-of-the-art transfer learning and domain adaptation algorithms. The results, demonstrated on both synthetic and real-world datasets, show that OBTL significantly enhances classification accuracy, particularly when the source and target domains are strongly related.
3. Scalability and Computational Efficiency: The paper highlights the computational challenges associated with hypergeometric functions, particularly in high dimensions. To address this, the authors implement a Laplace approximation technique to facilitate scalable computations without substantial loss in predictive performance.
4. Robustness to Hyperparameters: Through sensitivity analyses on synthetic data, the paper shows that while the framework's performance might be sensitive to the specification of prior relatedness between domains, it remains robust to other hyperparameter choices. This implies a level of flexibility and adaptability inherent in the proposed model.

Implications and Future Directions

The practical implications of this research are profound, particularly in fields like medical genomics, where obtaining labeled target data is expensive and challenging. The extension of this method to situations with limited labeled data is promising, given that many real-world applications would significantly benefit from the improved generalization capabilities enabled by OBTL.

Theoretically, this work reinforces the potential of Bayesian methodologies in transfer learning. The use of joint prior distributions and derived extended forms of hypergeometric functions illustrates a systematic approach to enhancing transferability insights between domains.

Future research could explore several areas of interest. One prominent direction involves extending the methodology to account for more complex relationships between domains, such as heterogeneous cases where feature spaces differ between source and target domains. Additionally, automating the characterization of domain relatedness, or "transferability," could significantly streamline applying the method across diverse datasets with minimal manual tuning. Another avenue is extending OBTL to multi-source transfer learning scenarios, where multiple source domains can be utilized to further refine and enhance the target domain's learner.

In summary, "Optimal Bayesian Transfer Learning" presents a meticulously developed framework that significantly progresses the transfer learning domain. It lays a robust foundation for both theoretical advancements and practical applications in various fields where data limitations pose persistent challenges.