Dr. Sebastian Jaimungal
Title: Minimal Kullback-Leibler Divergence and the Barycentre of Stochastic Processes
Date: Monday, April 15th, 2024
Time: 1:30PM (PDT)
Location: ASB 10900
Abstract: When models are trained on data alone, they may not accurately reflect a modeler鈥檚 view, an expert鈥檚 judgment, or user inputs. Moreover, on many occasions the experts disagree and thus their models, potentially trained on different datasets, need to be combined or sub-selected. To amalgamate the conflicting nature of experts鈥� views, we propose a modified Barycentre approach. Specifically, each expert proposes an n-dimensional stochastic process, and the combined meta model is created by penalising each expert鈥檚 model using a weighted relative entropy, where the weights may be proportional to an expert鈥檚 historical performance. We prove existence and uniqueness of the meta model, derive its dynamics, and develop a numerical algorithm for approximating the solutions. Furthermore, we allow the meta model to satisfy agreed upon external views, in which case the meta model is modified in a minimal manner to respect these external beliefs.