Daryl DeFord

Atticus McWhorter, Daryl DeFord

Novel Markov Chain Monte Carlo (MCMC) methods have enabled the generation of large ensembles of redistricting plans through graph partitioning. However, existing algorithms such as Reversible Recombination (RevReCom) and Metropolized Forest Recombination (MFR) are constrained to sampling from distributions related to spanning trees. We introduce the marked edge walk (MEW), a novel MCMC algorithm for sampling from the space of graph partitions under a tunable distribution. The walk operates on the space of spanning trees with marked edges, allowing for calculable transition probabilities for use in the Metropolis-Hastings algorithm. Empirical results on real-world dual graphs show convergence under target distributions unrelated to spanning trees. For this reason, MEW represents an advancement in flexible ensemble generation.

Jarren Briscoe, Garrett Kepler, Daryl Deford et al.

Evaluating machine learning models is crucial not only for determining their technical accuracy but also for assessing their potential societal implications. While the potential for low-sample-size bias in algorithms is well known, we demonstrate the significance of sample-size bias induced by combinatorics in classification metrics. This revelation challenges the efficacy of these metrics in assessing bias with high resolution, especially when comparing groups of disparate sizes, which frequently arise in social applications. We provide analyses of the bias that appears in several commonly applied metrics and propose a model-agnostic assessment and correction technique. Additionally, we analyze counts of undefined cases in metric calculations, which can lead to misleading evaluations if improperly handled. This work illuminates the previously unrecognized challenge of combinatorics and probability in standard evaluation practices and thereby advances approaches for performing fair and trustworthy classification methods.