Multi Marginal Optimal Transport

Multi-marginal optimal transport (MMOT) extends optimal transport theory to handle the optimal matching of multiple probability distributions simultaneously, aiming to find the most efficient way to align data across multiple views or modalities. Current research focuses on developing computationally tractable algorithms, such as adaptations of the Sinkhorn algorithm and novel approaches like genetic column generation, to overcome the computational challenges posed by the problem's inherent complexity, particularly in high-dimensional settings. MMOT finds applications in diverse fields, including machine learning (e.g., multi-view learning, adversarial training, and federated learning), network alignment, and the analysis of population flows, offering powerful tools for data analysis and model development in these areas.