Tripods/StemForAll2021 Research Projects

i) A learning theory perspective on Erdos type problems in combinatorial geometry

Project team: Alex Iosevich, Azita Mayeli, Brian McDonald and Emmett Wyman

Description: We are going to study the connections between the Vapnik-Chervonenkis dimension and problems in combinatorial geometry, such as the Erdos distance problem, the Szemeredi-Trotter incidence theorem and related topics. Roughly speaking, one can create learning tasks and natural families of classifiers such that when computing the VC-dimension, one encounters interesting point configuration problems that shed considerable amount of light on the aforementioned combinatorial problems.

Participants: Nathanel Grand and Maxwell Sun

ii) Neural networks and universal algebras

Project team: Charlotte Aten and Alex Iosevich

Description: .pdf

Participants: Nicholas Cimaszewski, Michele Martino, Svetlana Pack, Conor Taliancic, and Andrey Yao

iii) Neural networks with noise

Project team: Alex Iosevich and Steven Senger

Description: .pdf

Participants: Jordan Darefsky, Lucy Lin, George Lyu, Anna Myakushina, Edmund Sepeku, Maxwell Sun

iv) Neural networks and sales models with economic indicators

Project team: Alex Iosevich

Description: Many sales models starting returning less than stellar results during the Covid era, in part because the training data came from before the Covid period. In this project we are going to take several publically available data sets containing sales data and try to come up with the right mix of economic (and other) indicators that will make predictions as stable as possible across time, including the Covid period.

Participants: Nicholas O'Brien, Haiyan Huang, George Lyu, Kevin Xue, Kehan Yu, Kaiyuan Zhao, Stella Zhang

v) VC-dimension and neural networks

Project team: Ivan Chio, Alex Iosevich, Azita Mayeli, Andrew Thomas, and Emmett Wyman

Description: When we go over Chapter 20 (neural networks), we are going to see that neural networks are "universal approximators" in that any Lipschitz function can be approximated by a neural network arbitrarily closely. This is a fundamental result, but many real-life data sets are not realistically described by a Lipschitz function because the Lipschitz condition limits volatility. In this project we are going to explore the universal approximation in the case when Lipschitz functions are replaced by more complicated (and hopefully more realistic) classes of function, such as function with graphs satisfying a suitable fractal dimension condition.

Participants: Julie Fleischman, Filippo Iulianelli, Michele Martino, Svetlana Pack, Conor Taliancic, Nate Whybra, Kaiyuan Zhao

vi) Natural language processing on the social web

Project team: Alex Iosevich, Boris Iskra and Patricia Medina

Description: The idea of this project is to extract data from Twitter on certain topics, doing an NPL setup and performing and analyzing this social media data using machine learning techniques such as SVM, neural networks, and dimension reduction methods such as PCA and auto-encoders. Tools such as MongoDB will come in handy, and the participants will have the option of learning how to work on a given database in the cloud. The project is inspired by the presentations in the MAA-SIAM and TRIPODS Advanced Workshop in Data Science for Mathematical Sciences Faculty (ICERM) which used code based on "mining the Social Web" book by Matthew A. Russel. Several sets of code will be provided that will dictate the different milestones of the project.

Participants: Ivan Chio, Haiyan Huang, Zhiyu Lei, Lucy Lin,  Anna Myakushina, Edmund Sepeku, Siriu Wang

vii) Hype versus performance in the English football league

Project team: Alex Iosevich

Description: We are going to scrape the web for a news stories on players in the English football league and come up with a "hype metric" by rating how positive the stories are. We are also going to compile a variety of performance based metrics. We will then run a variety of neural network models to check how well the "hype metric" and performance ratings correlate.

Participants: Noah Boonin, Jordan Darefsky, Kevin Xue