Monroe Stephenson

Intro

Hello, I am Monroe Stephenson! I am currently pursuing my PhD in Applied Mathematics at the Berlin Mathematical School. My research focuses on the intersection of machine learning, algebraic statistics, and combinatorics. I am passionate about exploring how we can leverage these fields to solve complex real-world problems such as those in medical imaging and democratic decision-making mechanisms.

Feel free to explore my recent research, courses, and ongoing projects below!

Research

From 2023 to 2024, I worked as a Fulbright Scholar at the Max Planck Institute for Mathematics in the Sciences (MPI MiS) in Leipzig under the supervision of Bernd Sturmfels. My research focused on algebraic machine learning and statistical theory, particularly on non-independent component analysis and graphical models. This work led to the publication of Partitioned Independent Component Analysis, which is available on arXiv.

In the summer of 2022, I participated in an REU at the Hebrew University, where I worked under Karim Adiprasito, funded by his ERC Consolidator grant. We initially studied the Hopf Conjecture but soon discovered a generalization and simplification of Karim’s proof of the g-conjecture. Our method involved embedding simplicial complexes into the moment curve. Our draft is expected to be available on the arXiv soon.

In the summer of 2021, I participated in an REU at the University of Michigan under Jennifer Kenkel, Janet Page, and Daniel Smolkin, funded by Karen Smith’s NSF grant DMS-1801697. Our research focused on the differential power operation on ideals. We identified a class of monomial ideals in characteristic 0 whose differential powers are eventually principal. We also explored the containment problem between ordinary and differential powers of ideals and introduced a novel closure operation, called differential closure, which agrees with taking the radical of an ideal in simple D-modules. Our pre-print is available here.

In the summer of 2020, I participated in an altREU at Portland State University led by Christof Teuscher, created as a response to the COVID-19 pandemic. I collaborated with Art Duval from UTEP on applying the Abelian Sandpile Model to DDoS mitigation. This project led to an ongoing publication titled, "Analyzing Network Topology for DDoS Mitigation Using the Abelian Sandpile Model." You can find the final writeup here.

In the summer of 2019, I worked with Andrew Whitbeck at Texas Tech University in the Experimental High-Energy Particle department, contributing to the LDMX project. My work included SketchUp design, data collection from oscilloscopes, scintillators, and PMTs, and data analysis using Python. The project also involved designing and modifying electrical circuits. You can find my final writeup here.

Courses

I am currently enrolled in the following courses as part of my PhD studies:

• Statistical Methods for Data Science
• Analysis of High-Dimensional Data
• Stochastic Processes I: Discrete Time

These courses are designed to equip me with the advanced mathematical tools necessary for tackling problems in machine learning, data science, and high-dimensional statistics.

Work

Project Eaden – I work as a junior data scientist, contributing to a team that develops analytical tools for the food science industry. Our team has built a dashboard using Python and Dash to analyze experimental data from TPA and WB experiments. The dashboard provides:

• Data visualization through bar charts, line graphs, and interactive controls
• Filtering and exporting capabilities for in-depth data analysis
• Applying machine learning techniques for predictive modeling

In this role, I assist in applying machine learning models to optimize the data analysis process, helping enhance decision-making in experimental food science through AI-driven insights.

Telis Energy – As a GIS Intern, I used Python and PyQGIS to develop a script that automates wind turbine layout on GIS layers, ensuring maximum placement without overlap. This innovation optimized renewable energy projects by improving land use efficiency. I collaborated in a team focused on sustainable wind farm planning and environmental conservation efforts.

Personal Project – I am also working on a personal project that utilizes Graph Neural Networks (for ratings) and a Large Language Model (for reviews) to create a movie recommendation system for Criterion Channel films. This system aims to provide tailored recommendations based on user preferences and film characteristics.

Contact

Elements

i = 0;

while (!deck.isInOrder()) {
    print 'Iteration ' + i;
    deck.shuffle();
    i++;
}

print 'It took ' + i + ' iterations to sort the deck.';