Alexander Dukart

Adaptive Search Degrees of Freedom

This work introduces "Adaptive Search Degrees of Freedom" (ASDF) to quantify model complexity in modern, data-driven settings. Generalizing traditional Search Degrees of Freedom, the ASDF framework accommodates dynamic model-building procedures where the pool of candidate features evolves. By conceptualizing decision trees as adaptively-constructed, piecewise-constant models, this framework provides a unique lens to evaluate the inherent complexity of algorithms like CART and random forests, uncovering deeper insights into their mechanisms and predictive success.

Random Forests

My research investigates why random forests perform well across different signal-to-noise ratio (SNR) regimes. By studying the mechanisms that drive their success, I aim to uncover how random forests adapt to varying data environments and what this reveals about the role of regularization in machine learning.

Statistics Department Rankings

This project develops advanced statistical methods for ranking academic statistics departments. A key component of the work is creating new theoretical frameworks for understanding the statistics of tiers, which allow for more principled and robust comparisons across institutions.

Semantic similarity within ensemble tree methods

This project explores methods for grouping decision trees within ensemble tree models, based on semantic similarity. By identifying and analyzing clusters of trees that capture related predictive structures, the work aims to provide new insights into how ensembles represent information, improve interpretability, and potentially enhance model efficiency.

Allegheny County Fire Incident Spatial & Statistical Analysis

This comprehensive spatial and statistical analysis examines over 2,200 fire incidents investigated by the Allegheny County Fire Marshal. The project establishes a geographic baseline through an interactive web map (Leaflet.js) to visualize regional distribution and response accessibility. Beyond spatial mapping, the research utilizes regex text-mining on investigator summaries to uncover hidden ignition trends and deploys regularized predictive modeling to identify socio-economic drivers of fire rates.

Bayesian Statistics Project: Predicting OPS

This project implements a Bayesian Hidden Markov Model (HMM) to model the career performance trajectories of MLB players, specifically focusing on On-base Plus Slugging (OPS). Markov Chain Monte Carlo (MCMC) simulations were utilized to estimate the posterior distributions of latent performance states, allowing the identification of elite player cohorts. The methodological framework adapts the modeling approach established by Jensen et al. (2009).

Legislative Transparency and Prediction

Motivated by the opacity of the U.S. legislative process stemming from the immense volume of annual bill proposals, this research developes a predictive framework utilizing Natural Language Processing (NLP) to forecast bill enactment. The methodology incorporates BERT word embeddings and applies advanced machine learning techniques to bag-of-words models. Results indicate that this approach predicts legislative passage with a high degree of accuracy.

NFL Big Data Bowl 2026: Swooping In

This project introduces a machine learning framework to evaluate NFL secondary players by analyzing spatial positioning and tracking data. By employing gradient-boosted models, the researchers quantify specific "Anticipation" (pre-throw) and "Reaction" (post-throw) metrics to calculate a defender's probability of successfully impacting a play. The study further validates player reliability by applying conformal prediction to establish lower bounds on success probabilities, ensuring that high performance metrics reflect consistent skill rather than statistical noise.

Evaluating large language models capacity to reason

Doctor bias against children with type 2 Diabetes

Covid19 Vaccine Resistance