Uniform Transformation of Non-Separable Probability Distributions
This work addresses a foundational challenge in probability theory and machine learning for researchers dealing with high-dimensional data transformations, though it appears incremental as it builds on existing cumulative distribution concepts.
The paper tackles the problem of uniformly transforming non-separable probability distributions in higher dimensions, where traditional cumulative distribution methods fail, by developing a theoretical framework using a potential function and a numerical method to compute it, with examples demonstrated in two dimensions.
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher dimensions, or non-separable distributions. A potential function is shown to link probability density functions to their transformation, and to generalize the cumulative. A numerical method is developed to compute the potential, and examples are shown in two dimensions.