Cramer Wold Distance

The Cramer-Wold distance is a method for comparing high-dimensional probability distributions by analyzing their projections onto one-dimensional lines. Current research focuses on improving its application in generative models, particularly by incorporating both marginal and joint distributional information, leading to the development of novel architectures like Cramer-Wold Distributional Autoencoders. This approach addresses limitations of existing methods in handling complex correlations within high-dimensional data, enhancing the accuracy and efficiency of synthetic data generation and improving the training of models like Gaussian Mixture Models via gradient descent. The resulting advancements have implications for various fields, including data privacy, reinforcement learning, and other applications requiring accurate distributional modeling.