Fall 2019 Postdoc Seminar Series
October 16, 2019 –
Talk Title: (1) Drivers Learn City-scale Dynamic Equilibrium (2) Probability Estimation on Manifolds via Diffusion
Speaker: Ruda Zhang, First-Year SAMSI Postdoctoral Fellow
The first part is to prepare for a talk at INFORMS 2020 next week. This paper studies the taxi industry as a game of multi-market competition among firms of equal capacity, where taxi drivers allocate service time across the street network to maximize income. We prove that the game has a Nash equilibrium, which is symmetric, essentially unique, and globally asymptotically stable under gradient adjustment process and imitative learning. With 2009-2013 trip records of New York City yellow cabs, we validate that taxi drivers’ behavior conforms to our prediction, and that drivers learn the equilibrium strategy over time.
The second part proposes a method for approximating probability distributions on manifolds. Recent advances in statistics and machine learning have exploited the low-dimensional manifold structure of high-dimensional data sets. Being able to estimate probability distributions on such manifolds allows for generative models (i.e. sampling) and statistical inference. With heat diffusion as a unifying concept for density estimation on Euclidean spaces and non-trivial manifolds, our paper solves this task using an approximate Neumann heat operator.
No references provided at this time