Resource Allocation and Statistical Estimation in Epidemic Networks: Scalable Algorithms and Analysis
Abstract
Major Goals: Our proposed research will advance the frontiers of stochastic modeling for dynamic networks. We will analyze problems in influence maximization, fractional immunization and boosting, and detection and estimation, with the unifying theme of devising computationally efficient algorithms with rigorous mathematical guarantees for allocating resources and estimating characteristics of time-varying networks. This work significantly generalizes and extends existing approaches in network science by allowing greater flexibility in modeling epidemics and interventions. In particular, we will depart from standard submodularity assumptions known to be irreflective of real-world cascades, and allow targeted interventions to be fractional rather than binary. We will also develop algorithms suited to incorporate uncertainty about network connectivity, and provide methods for estimating graph characteristics based on sensor data. Accomplishments: Two directions were primarily explored in this project. The first was most closely aligned with the original plan for the project. One PhD student worked on developing new methods for resource allocation in networks under a "fractional immunization" framework. This mostly consisted of formulating the allocation problem as a constrained optimization problem in terms of eigenvalues of the underlying graph structure. The student then studied the performance of the proposed algorithm under various network structures, focusing on optimality and stability of the algorithm. Analogies in the "fractional boosting" problem were also explored. However, work on this project ended up stalling for quite a while, due to personal and family problems that the student encountered after the pandemic began. The second student who was recruited to help with the project had prior interest in the theory of deep learning. Thus, he worked on a problem which was more abstractly connected to the goals of the project.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 15, 2021
- Accession Number
- AD1208086
Entities
People
- Michael Liou
- Po-ling J. Loh
Organizations
- University of Wisconsin–Madison