Relative Distributions and Their Connection to Optimal Transport

Hector Escandon Vanegas
MS, 2023
Handcock, Mark S
Relative Distributions and Optimal Transport are versatile and widely used tools across various industries and fields. Relative Distributions are adept at gauging the disparities in ratios between two distributions. At the same time, Optimal Transport provides a deep understanding of the differences between distributions based on the amount of mass required to equalize them. Individuals have made past efforts to incorporate specific techniques into already established models for Statistics, Machine Learning, and Artificial Intelligence. Thus far, there has been an absence of any conclusive correlation between these two domains despite multiple individual endeavors. We have linked Relative Distributions with Optimal Transport, using various distributions to analyze distribution variation precisely. When dealing with Relative Distributions, our one-to-one distributions become Uniform, and the Optimal Transport method generates a Matrix that indicates how these inequalities should be adjusted. Our research indicates that our model may surpass other commonly used models, potentially promoting the implementation of similar approaches across multiple fields.
2023