Department of Mathematics Cornell University Senior Thesis
The focus of this senior thesis will be Determinantal Point Processes (DPPs), encompassing an exploration of background information, applications, and simulations to validate findings within the field. In the introductory section, I aim to provide definitions of various types of DPPs, highlight their properties, and present relevant theorems. A specific emphasis will be placed on the Descents in Random Sequence DPP. We will show how one can find metrics that verify that the kernel representation is accurate when compared to empirical simulations.
We will also provide a brief introduction into the Charlier ensemble DPP. There has been no formal verification of computer simulations of checking to see if the sampling from the kernel of these two processes results in similar results as empirical implementations. Lastly, I will explore the applications of DPPs, particularly within the realm of machine learning, a domain that has recently attracted increased attention.
I gave a talk to the Cornell Univeristy Math Club. Here is the link.