A Short Introduction to Optimal Transport and Wasserstein Distance
2 days ago
- #machine-learning
- #wasserstein-distance
- #optimal-transport
- Optimal transport theory provides a method to measure distances between probability distributions, addressing limitations of KL divergence.
- The Wasserstein distance, or Earth Mover's Distance, is symmetric and satisfies the triangle inequality, making it a robust metric.
- Optimal transport can be visualized through physical analogies like moving dirt to fill holes, with costs based on distances.
- Discretizing the problem allows solving optimal transport via linear programming, making it computationally tractable.
- Entropy regularization is a key innovation that simplifies computation by penalizing low-entropy transport plans.
- Applications of optimal transport span machine learning, imaging, generative models, and biological data analysis.