Learning to share: Bayesian approaches to sparsity and transfer

In an age of increasingly complex, high-dimensional, and scarce data, sharing information across variables, tasks, and datasets, is critical to building models that are effective. This thesis explores Bayesian approaches to sparsity and transfer learning that utilize information present within different aspects of available data to construct models that are more efficient and interpretable. We utilize the Bayesian framework's inherent ability to integrate prior knowledge with new data, enabling information sharing to get informed posterior distributions. Our first contribution pertains to high-dimensional settings, where both the number of responses and covariates is substantial, and the responses themselves are interdependent. In such scenarios, we introduce a novel Bayesian methodology for simultaneous variable selection and sparse precision matrix estimation using high-dimensional Gaussian graphical models. Our approach provides sparse estimates for three distinct structures: the regression coefficient matrix, the conditional dependency structure among responses, and the relationships between responses and covariates. Together, these parameters offer a complete picture of the relationship between the responses and the covariates. Our second contribution involves collaboration with Mosquito Abatement Districts (MADs) in the Chicago metropolitan area and its suburbs to develop efficient models for West Nile Virus (WNV) surveillance. First, we propose a three-phase framework to identify optimal locations for mosquito traps, which can then inform about the risk of infection. This framework assists the MADs in reducing the number of traps required while making each individual trap more efficient. Next, we focus on predicting the human risk of WNV using trap-derived data. We illustrate that predicting the Vector Index (VI), a commonly used measure of WNV risk, is insufficient by itself. Instead, accurately predicting VI's underlying components—abundance and infection rates—simultaneously provides a clearer basis for targeted interventions. We employ the Bayesian framework developed earlier to obtain improved predictions of these components, thereby enabling mosquito prevention programs to make better-informed decisions. Our final contribution focuses on sharing information between models. Specifically, we propose a semi-supervised, source-free transfer learning approach based on power priors. By generating pseudo-labeled source data from a black-box model and combining it with a small labeled target dataset, we derive a posterior update that allows adaptive transfer without requiring direct access to source data or internal parameters of pre-existing models. Overall, this thesis integrates theoretical advancements with practical statistical applications. Collaborations with public health organizations illustrate the practical effectiveness of our information-sharing methodologies, demonstrating significant improvements in statistical modeling. Ultimately, this work underscores the importance of adopting information sharing as a fundamental statistical principle to better handle increasingly complex and rich datasets.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Chakravarti, Anwesha

Contributors dc:contributor

• Liang, Feng
• Smith, Rebecca Lee
• Li, Bo
• Wang, Yuexi

• Bayesian Methodology
• Graphical Models
• Bayesian Variable Selection
• Bayesian Regularization
• West Nile Virus
• Mosquito Surveillance
• Bayesian Transfer Learning
• Semi-supervised Learning

Statement dc:rights

• Copyright 2025 Anwesha Chakravarti

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129923

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129923