Recent Advances in Bayesian Transfer Learning

Verbal autopsy (VA) algorithms are routinely employed in low- and middle-income countries to determine individual causes of death (COD). They are then aggregated to estimate population-level cause-specific mortality fractions (CSMFs), which are essential for public health policymaking. However, VA algorithms often misclassify COD, introducing bias in CSMF estimates. A recent method, VA-calibration, addresses this bias by utilizing a VA misclassification rate matrix derived from limited labeled COD data collected in the CHAMPS project. Due to limited labeled samples, the data are pooled across countries to improve estimation precision, thereby implicitly assuming uniform misclassification rates. In this presentation, I will highlight substantial cross-country heterogeneity in VA misclassification, challenging this homogeneity assumption and revealing its impact on VA-calibration bias. To address this, I will propose a comprehensive country-specific VA misclassification matrix modeling framework in data-scarce settings. The framework introduces a novel base model that parsimoniously characterizes the misclassification matrix through two latent mechanisms: intrinsic accuracy and systematic preference. We theoretically prove that these mechanisms are identifiable from the data and manifest as a form of invariance in misclassification odds, a pattern evident in the CHAMPS data. Building on this, the framework then incorporates cross-country heterogeneity through interpretable effect sizes and uses continuous shrinkage to balance the bias-variance tradeoff in misclassification matrix estimation. This effort broadens VA-calibration's future applicability and strengthens ongoing efforts of using VA for mortality surveillance. I will illustrate this through applications to mortality surveillance projects, such as COMSA in Mozambique and CA CODE.
 

Transfer learning allows an analyst to borrow information from plentiful historical datasets to improve model behavior on a limited target dataset. Incumbent transfer learning methods proceed by 1) estimating baseline parameters using the entire combined data before 2) fitting parameters to the target dataset while penalizing their difference from the baseline parameters. However, the fact that the baseline parameters depend on the data precludes their use for prior parameterization in the formal Bayesian setting. In this talk, we will instead propose to parameterize the prior via the expected log-likelihood maximizer under a given parameter setting, which removes the data-dependence from the prior. We show how to deploy this prior to conduct Bayesian model selection for determining which historical datasets are relevant to the problem at hand in the generic likelihood setting, including correlated error structures. We also discuss computational aspects of posterior simulation via convex optimization and our motivating application of emerging forced human migration crises. 

Transfer learning uses a data model, trained to make predictions or inferences on data from one population, to make reliable predictions or inferences on data from another pop- ulation. Most existing transfer learning approaches are based on fine-tuning pre-trained neural network models, and fail to provide crucial uncertainty quantification. We develop a statistical framework for model predictions based on transfer learning, called RECaST. The primary mechanism is a Cauchy random effect that recalibrates a source model to a target population; we mathematically and empirically demonstrate the validity of our RECaST approach for transfer learning between linear models, in the sense that prediction sets will achieve their nominal stated coverage, and we numerically illustrate the method's robustness to asymptotic approximations for nonlinear models. Whereas many existing techniques are built on particular source models, RECaST is agnostic to the choice of source model, and does not require access to source data. For example, our RECaST transfer learning approach can be applied to a continuous or discrete data model with lin- ear or logistic regression, deep neural network architectures, etc. Furthermore, RECaST provides uncertainty quantification for predictions, which is mostly absent in the literature. We examine our method's performance in a simulation study and in an application to real hospital data. 

Statistical transfer learning has gained interest among statisticians and data scientists in the recent years. While the idea of using a priori knowledge is not new in statistics, transfer learning formalizes the concept of leveraging information from related data domains in order to improve modeling and prediction for a given learning task. Statisticians have explored the ideas of transfer learning with focus on improving inference and prediction and to this end, they have made substantial contributions to the literature. In this talk, after a review of statistical transfer learning with a focus on Bayesian approaches, we will discuss the recent advances in the literature with focus on papers presented at this session. We will also discuss challenges and future work in this area.