Frederick "Forrest" Miller

About Me

I am a PhD Student at Northeastern University Department of Mathematics in the Northeastern University Robust Autonomy Lab (NEURAL) under Professor David Rosen. I am interested in exploring the depths of mathematical optimization and its applications. In particular, I am exploring developing efficient algorithms to solve semi-algebraic optimization problems that arise in machine intelligence.

Outside of mathematics, I like watching movies and going hiking through New England.

Education

• PhD in Mathematics, Northeastern University. Fall 2023 - Present

• Bachelor of Science in Mathematical Sciences, Worcester Polytechnic Institute (WPI), August 2019 - May 2023. GPA: 3.92/4.0
• Bachelor of Science in Data Science, Worcester Polytechnic Institute (WPI), August 2019 - May 2023. GPA: 3.92/4.0
  • Major Qualifying Project (MQP) (Senior Thesis): “Deep Learning for Reflected Backwards Stochastic Differential Equations”, Advisor: Stephan Sturm. Awarded MQP Departmental Honorable Mention

Research Interests

My current research involves developing novel algorithms to solve large scale semialgebraic optimization problems. Towards this effort, I was awarded the National Science Foundation Graduate Research Fellowship (NSF GRFP). To get a flavor of my research, check out my research proposal to the GRFP! In short, we hope to develop algorithms and software that can take a large scale polynomial optimization problem and construct and solve its associated SDP relaxation. One key technique we are applying is the Lasserre / Sum of Squares hierarchy for polynomial optimization problems, which is a tool for solving polynomial optimization problems through a sequence of semidefinite relaxations.

In addition, I am particularly interested in developing solutions where the problem data may be contaminated with outliers. Currently, many algorithms are brittle to outliers, but we hope to bridge this gap by developing robust algorithms for these problems.

As an undegraduate, I conducted research in public sector operations research. This involved applying mixed integer linear fractional programming to the problem of marginal shelter deployment for a city. Additionally, I researched deep learning techniques for determining the solution to a certain class of stochastic differential equations for the problem of option pricing in mathematical finance.

Skills

• Programming Languages: Python, Julia, MATLAB, R, SQL, LaTeX
  • Some of my favorite packages: pandas, numpy, matplotlib, scikit, gurobi, tensorflow, pytorch
• Solvers: Gurobi, Mosek, COSMO, Clarabel
• Applications: Github, Slurm, Overleaf, Microsoft Office, Google Suite

Selected Courses:

As a graduate student at Northeastern University

• Mathematics - Optimization and Complexity, Analysis 2, Algebra 1, Readings in Random Matrix Theory and Compressed Sensing, Geometry and Applications of Tensors

As an undergraduate at Worcester Polytechnic Institute:

• Mathematics - Computational Optimization, Convex Optimization, Linear Programming, Data Analytics and Statistical Learning, Top Algorithms in Applied Mathematics, Numerical Methods for Linear and Nonlinear Systems, Probability Theory, Linear Algebra (Graduate), Lebesgue Measure and Integration (Graduate), Portfolio Valuation and Risk Management (Graduate), Matrices and Linear Algebra II, Combinatorics, Applied Statistics I & II
• Computer Science -Analysis of Algorithms, Machine Learning, Database Systems I, Accelerated Introduction to Program Design, Object Oriented Design Concepts
• Data Science - Advanced Prescriptive Analytics, Modeling and Data Analysis, Introduction to Data Science, Computational Data Intelligence

Publications

• Larson, D.M., Bungula, W., Lee, A., Stockdill, A., McKean, C., Miller, F. I., Davis, K., Erickson, R.A. and Hlavacek, E. (May 2023), Reconstructing missing data by comparing interpolation techniques: Applications for long-term water quality data. Limnology and Oceanography: Methods.
• Larson D.M., Bungula W., McKean C., Stockdill A., Lee A., Miller, F. I., Davis, K. (June 2023) Quantifying ecosystem states and state transitions of the Upper Mississippi River System using topological data analysis. PLoS Computational Biology 19(6): e1011147.
• Miller, F. I., Y. Kaya, G. L. Dimas, R. Konrad, K. L. Maass, A. C. Trapp. (April 2023) Optimizing the Benefit to Cost Ratio for Public Sector Decision Making
• Hoehn, K. B., Turner, J. S., Miller, F. I., Jiang, R., Pybus, O. G., Ellebedy, A. H., & Kleinstein, S. H. (2021). Human B cell lineages associated with germinal centers following influenza vaccination are measurably evolving. ELife, 10, e70873.

Presentations

• Northeastern Graduate Student Seminar @ Northeastern
  • Certifiable Estimation Through Semidefinite Programming, An Introduction to Mathematical Finance
• Mathematical Finance and Stochastic Analysis Seminar @ WPI
  • Risk Indifference Pricing for American Put Options
• WPI PhD Student Seminar, January 2023
  • Modern Portfolio Theory from Scratch
• 2023 Joint Mathematics Meeting, January 2023 - Optimizing the Benefit-to-Cost Ratio for Public Sector Decision Making
• 2022 INFORMS Annual Meeting, October 2022
  • Optimizing The Benefit-to-Cost Ratio For Effective Capacity Deployment For New York City’s Homeless Youth Shelter System
  • Awarded INFORMS Scholarship to be funded and attend the conference and attend special sessions
• ARCHES Lab talk @ WPI, August 2022
  • Preliminary version of “Optimizing The Benefit-to-Cost Ratio For Effective Capacity Deployment For New York City’s Homeless Youth Shelter System”
• WPI PhD Student Seminar @ WPI, February 2022
  • A brief survey of operations research and optimization
• Math REU Poster Session @ University of Wisconsin - La Crosse (UWL), August 2021
  • Research poster to members of UWL Math & Biology Departments
• WPI Math Club Sunday Night Seminar - April 2020
  • Introductory combinatorics to members of WPI Math club
• WPI Math Department Open House - April 2021, October 2021, April 2022
  • Mathematical Sciences undergraduate program at WPI with prospective students

Awards

• National Science Foundation Graduate Research Fellowship (NSF GRFP) - Awarded three full years of funding for my doctoral research. Here is my personal statement.
• WPI Peer Learning Assistant of the Year 2023
  • Also awarded Peer Learning Assistant of the year within the Mathematical Sciences Department
• WPI MQP Award Departmental Honorable Mention for Senior Thesis
• WPI Senior Math Award 2023
  • Awarded for outstanding performance and making valuable contributions to the WPI Community
• INFORMS Scholarship Award: Funding to travel and present at the INFORMS Annual Meeting, 2022
• Full funding to attend SIAM Summer School on Financial Analytics in L’Aquila, Italy
• WPI Presidential Scholarship (2019 - 2023)
• Dean’s List, WPI

Teaching and Mentoring Experience

From May 2024 to July 2024, I served as a mentor to two undergraduate students. Together, we explored how to perform large scale eigenvalue computations.

Additionally, I served as Peer Learning Assistant (PLA) for the Mathematical Sciences Department at WPI from August 2020 to May 2023. This entails:

1. Manage a section of 20 to 35 students in mathematical sciences courses at WPI
2. Run a weekly discussion section reviewing lecture content
3. Grade Homework & exams for the section working with a Professor and other PLAs and Teaching Assistants

Courses PLA’d:

• MA 3231 - Linear Programming, A Term 2022
• MA 2621 - Probability for Applications, C Term 2022, D Term 2023
• MA 2071 - Matrices & Linear Algebra I - B Term 2020, D Term 2021
• MA 2072: Accelerated Matrices & Linear Algebra I - C Term 2023
• MA 1023 - Calculus III, A Term 2020, A Term 2021, D Term 2022, B Term 2022

Leadership

• Lab Meeting Organizer, NEU-RAL (August 2023 - August 2024)
  • Organized Lab Presentations for members of NEU-RAL to share their work.
• President, WPI Math Club (April 2020 - March 2023)
  • Lead meetings for WPI’s math club by finding an activity for our weekly math hour. Normally this consists of a fun puzzle with a mathematical bent that the club discusses and tries to solve.
• President, WPI Pi Mu Epsilon Massachusetts Alpha Math Honors Society (May 2022 - May 2023)
  • Vice President January 2022 - May 2022, Member April 2021 - January 2022

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