René's URL Explorer Experiment

{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"Error in the definition of the Wasserstein distance from the user guide","articleBody":"## Describe the bug\nI have found a typo in the user guide which can be quite misleading. \n\nThe Wasserstein distance should be defined for a specific metric $$d$$ on the real numbers, e.g., the Euclidean norm, and a specific order $$p$$. \n\nThe definition given in the documentation is as follows:\n\n$$  W_p(a,b)=(\\min_{\\gamma \\in \\mathbb{R}_+^{m\\times n}} \\sum_{i,j}\\gamma_{i,j} \\|x_i-y_j \\|_p)^\\frac{1}{p}$$\n\n$$ s.t. \\gamma 1 = a; \\gamma^T 1= b; \\gamma\\geq 0 $$\n\nThe order- $$p$$ should be a power of the metric $$d$$.\n\n\nSee [link to documentation](https://pythonot.github.io/user_guide.html#computing-wasserstein-distance).\n\nTo be exact, we would need a definition such as :\n\n$$  W_p(a,b)=(\\min_{\\gamma \\in \\mathbb{R}_+^{m\\times n}} \\sum_{i,j}\\gamma_{i,j}d(x_i,y_j)^p)^\\frac{1}{p}$$\n\n$$ s.t. \\gamma 1 = a; \\gamma^T 1= b; \\gamma\\geq 0 $$\n\nOr if $$d$$ is specifically defined as any arbitrary norm $$\\|\\cdot\\|$$ on the real numbers:\n\n$$  W_p(a,b)=(\\min_{\\gamma \\in \\mathbb{R}_+^{m\\times n}} \\sum_{i,j}\\gamma_{i,j}\\|x_i-y_j\\|^p)^\\frac{1}{p}$$\n\n$$ s.t. \\gamma 1 = a; \\gamma^T 1= b; \\gamma\\geq 0 $$\n\nThanks for your time.\n\n\n\n\n\n\n\n","author":{"url":"https://github.com/jupall","@type":"Person","name":"jupall"},"datePublished":"2025-11-10T14:25:05.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":1},"url":"https://github.com/779/POT/issues/779"}