Luke P

I’m a machine learning research assistant with a strong foundation in applied mathematical sciences and economics, and a focus on rigorous statistical learning theory. I enjoy translating theory into reliable empirical evidence through careful modeling and simulation.

At Texas State University’s Math REU (Machine Learning Group), I designed and implemented a novel Lazy Variable Importance framework extending feature-selection methods for deep ReLU networks from regression to binary classification. I derived theoretical predictive error bounds using a three-term decomposition (approximation, estimation, and linearization error), then built a large-scale empirical simulation pipeline in Python with PyTorch Lightning and Scikit-learn to validate the results.

Through an independent study at the University of Connecticut’s Department of Mathematics, I worked through PAC learnability, ERM, convex learning, SGD, and DNNs, and presented findings at the UConn Mathematics DRP Conference to communicate complex ideas clearly. My approach blends mathematical precision with practical clarity so the work stays both correct and usable.

In independent research on FOMC Rate Shocks & U.S. Equity Sector Returns, I estimated OLS regressions across FOMC announcement dates to quantify heterogeneous sector sensitivities, controlling for market volatility (VIX) and Treasury term spread. I built my data pipeline in Python (yfinance, fredapi, statsmodels, matplotlib) and delivered results via sector coefficient plots and robustness tables.