📐 New preprint by Gabriel Peyré: The paper introduces a new class of spectral #Wasserstein distances, linking #OptimalTransport with normalized #gradient methods. It shows that spectrally normalized #GradientDescent can be interpreted as a gradient flow in this spectral-W geometry, providing a principled bridge between #optimization dynamics and transport metrics:
🌟 Sinkhorn-Knopp Algorithm: Giải thuật này như Softmax nhưng专注 về transport tối ưu trong toán học. Tài liệu liệt kê #SinkhornKnoppAlgorithm #OptimalTransport #AI #ToánHọc #MachineLearning
https://www.reddit.com/r/programming/comments/1oc3ond/sinkhornknopp_algorithm_like_softmax_but_for/
A short introduction to optimal transport and Wasserstein distance
https://alexhwilliams.info/itsneuronalblog/2020/10/09/optimal-transport/
#HackerNews #optimaltransport #Wasserstein #distance #machinelearning #math #statistics #dataanalysis
The #Wasserstein distance (#EMD), sliced Wasserstein distance (#SWD), and the #L2norm are common #metrics used to quantify the ‘distance’ between two distributions. This tutorial compares these three metrics and discusses their advantages and disadvantages.
🌎 https://www.fabriziomusacchio.com/blog/2023-07-26-wasserstein_vs_l2_norm/
In machine learning, especially when dealing with probability distributions or deep generative models, different metrics are used to quantify the ‘distance’ between two distributions. Among these, the Wasserstein distance (EMD), sliced Wasserstein distance (SWD), and the L2 norm, play an important role. Here, we compare these metrics and discuss their advantages and disadvantages.
This tutorial takes a different approach to explain the #Wasserstein distance (#EMD) by approximating the #EMD with cumulative distribution functions (#CDF), providing a more intuitive understanding of the metric.
🌎 https://www.fabriziomusacchio.com/blog/2023-07-24-wasserstein_distance_cdf_approximation/
In the previous two posts, we’ve discussed the mathematical details of the Wasserstein distance, exploring its formal definition, its computation through linear programming and the Sinkhorn algorithm. In this post, we take a different approach by approximating the Wasserstein distance with cumulative distribution functions (CDF), providing a more intuitive understanding of the metric.
Calculating the #Wasserstein distance (#EMD) 📈 can be computational costly when using #LinearProgramming. The #Sinkhorn algorithm provides a computationally efficient method for approximating the EMD, making it a practical choice for many applications, especially for large datasets 💫. Here is another tutorial, showing how to solve #OptimalTransport problem using the Sinkhorn algorithm in #Python 🐍
🌎 https://www.fabriziomusacchio.com/blog/2023-07-23-wasserstein_distance_sinkhorn/
Calculating the Wasserstein distance can be computational costly when using linear programming. The Sinkhorn algorithm provides a computationally efficient method for approximating the Wasserstein distance, making it a practical choice for many applications, especially for large datasets.
The #Wasserstein distance 📐, aka Earth Mover’s Distance (#EMD), provides a robust and insightful approach for comparing #ProbabilityDistributions 📊. I’ve composed a #Python tutorial 🐍 that explains the #OptimalTransport problem required to calculate EMD. It also shows how to solve the OT problem and calculate the EMD using the Python Optimal Transport (POT) library. Feel free to use and share it 🤗
🌎 https://www.fabriziomusacchio.com/blog/2023-07-23-wasserstein_distance/
The Wasserstein distance, also known as the Earth Mover’s Distance (EMD), provides a robust and insightful approach for comparing probability distributions and finds application in various fields such as machine learning, data science, image processing, and information theory. In this post, we take a look at the optimal transport problem, required to calculate the Wasserstein distance, and how to calculate the distance metric in Python.
#OptimalTransport: Moving stuff through a #labyrinth
(Nicolas Papadakis: Optimal Transport for Image Processing, Signal and Image Processing. Université
de Bordeaux; Habilitation thesis, 2015. tel-01246096v8, 2007)
Fabrizio Musacchio
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