Learning and Optimization over Abstract Non-Manifold Structures: A Case in Biological Data Analysis

Explore the intersection of optimization theory and biological data analysis in this one-hour lecture by Thien Le, a PhD student at MIT CSAIL. Delve into the challenges of optimizing over complex combinatorial and geometric structures that arise in phylogenetic studies. Examine how maximum likelihood analysis models evolution as a parametric stochastic process, and investigate the non-manifold nature of tree structures in evolutionary relationships. Discover known results on the algebro-geometric properties of this space and learn how smooth optimization techniques can be applied to develop more efficient algorithms and heuristics for phylogenetic problems. Gain insights into ongoing research that combines mathematical theory with practical applications in biological data analysis.