Research

Machine Learning

• Random Matrix Initialization Methods in Machine Learning, May 2021
  • [PDF]: Used randomized initialization methods to improve performance of 2-layer feed forward neural networks
• An Overview of the Nested Sampling Algorithm, May 2023, P. Hoffman, supervised by Professor Peter Kempthorne.
  • [PDF]: Studied the Nested Sampling algorithm and its application to calculating the normalizing factor in Bayesian statistics

 

Optimization

• Current research uses polyhedral lifts and flow decompositions on layered graphs to effeciently solve variants of the two-person Blotto game from game theory using a polynomial size linear program, supervised by Professor Pablo Parrilo

• Integer Programming Solutions to Graph Coloring, May 2022, P. Hoffman, supervised by Professor James Orlin.

  • Designed an integer program to find proper colorings of randomly constructed non-planar graphs
  • [PDF]:

 

Combinatorics

• Expander Graphs and their Construction, May 2022, P. Hoffman.
  • Proved the existence of expander graphs using randomized constructions and proved the unique neighbor expansion
  • [PDF]:
• Polygon Dynamics Under Reflection Operations, December 2022, P. Hoffman with O. Lores & C. Yung.
  • Studied the dynamics of a polygon as its vertices are iteratively reflected across the perpendicular bisector of their neighbors
  • [PDF]: