[Paper Review] Bayesian Transfer Learning

Piotr M. Suder, Jason J. Xu+1 more|arXiv (Cornell University)|Dec 20, 2023

Domain Adaptation and Few-Shot Learning4 citations

TL;DR

This paper presents a comprehensive survey of Bayesian transfer learning methods that leverage prior knowledge from related domains to improve inference and prediction in data-scarce target domains. By employing hierarchical models, shared latent spaces, and structured priors, Bayesian approaches enable coherent uncertainty quantification and robust handling of negative transfer, outperforming frequentist competitors in simulation studies on covariance and precision estimation.

ABSTRACT

Transfer learning is a burgeoning concept in statistical machine learning that seeks to improve inference and/or predictive accuracy on a domain of interest by leveraging data from related domains. While the term "transfer learning" has garnered much recent interest, its foundational principles have existed for years under various guises. Prior literature reviews in computer science and electrical engineering have sought to bring these ideas into focus, primarily surveying general methodologies and works from these disciplines. This article highlights Bayesian approaches to transfer learning, which have received relatively limited attention despite their innate compatibility with the notion of drawing upon prior knowledge to guide new learning tasks. Our survey encompasses a wide range of Bayesian transfer learning frameworks applicable to a variety of practical settings. We discuss how these methods address the problem of finding the optimal information to transfer between domains, which is a central question in transfer learning. We illustrate the utility of Bayesian transfer learning methods via a simulation study where we compare performance against frequentist competitors.

Motivation & Objective

• To address the challenge of optimal information transfer between related statistical domains, especially when target data are limited.
• To highlight underappreciated Bayesian approaches that naturally incorporate prior knowledge, offering a principled alternative to frequentist transfer learning.
• To demonstrate the utility of Bayesian methods in mitigating negative transfer through structured modeling and uncertainty quantification.
• To provide a taxonomy of Bayesian transfer learning methods applicable to high-dimensional and complex data settings.
• To identify promising research directions, particularly in deep learning and nonparametric models.

Proposed method

• Utilizes hierarchical and random effects models to share information across domains while allowing for domain-specific variation.
• Employs shared latent space models, such as multi-study factor analysis, to enable transfer in high-dimensional data with common underlying structures.
• Applies shrinkage priors and sparsity-inducing penalties (e.g., L1 norms) to promote robust estimation of covariance and precision matrices.
• Uses posterior inference to provide coherent uncertainty quantification, including credible intervals for functionals of covariance matrices.
• Adapts methods like SUFA (a Bayesian factor model) and MT-Glasso (multi-task graphical lasso) for transfer learning, even when not originally designed for the task.
• Employs simulation studies to compare Bayesian methods against frequentist counterparts, evaluating performance via Frobenius and L1 norm errors.

Experimental results

Research questions

• RQ1 How can Bayesian hierarchical models be adapted to enable effective and principled knowledge transfer across related statistical domains?
• RQ2 What role do shared latent spaces play in improving inference in low-sample-size target domains?
• RQ3 How do Bayesian methods compare to frequentist transfer learning approaches in terms of estimation accuracy and robustness?
• RQ4 In what ways can uncertainty quantification be naturally embedded in Bayesian transfer learning frameworks?
• RQ5 What are the key challenges in avoiding negative transfer, and how can Bayesian modeling help control the strength and structure of information transfer?

Key findings

• The Bayesian method SUFA outperformed frequentist competitors MT-Glasso and Trans-CLIME in estimating covariance and precision matrices, particularly in terms of stability and accuracy.
• SUFA provided reliable posterior distributions over positive semidefinite covariance matrices, enabling uncertainty quantification for any functional of interest.
• Despite being designed for covariance estimation, SUFA also yielded competitive precision matrix estimates, demonstrating robustness across related tasks.
• Trans-CLIME produced unstable and often non-invertible precision matrices, limiting its practical utility in covariance estimation.
• MT-Glasso produced invertible matrices but yielded estimates further from the truth than SUFA, indicating suboptimal performance.
• The simulation results show that Bayesian transfer learning with structured priors can effectively mitigate negative transfer and improve estimation in high-dimensional, low-sample regimes.