Following up on this, I also explored a more direct use of #WassersteinDistance in #WGANs: Instead of training a discriminator, the generator is optimized by explicitly computing the #OptimalTransport distance between real and generated samples. This turns the loss into the actual metric of interest and removes the adversarial setup, leading to a more direct and stable training signal. And we can generate cool animations, too ^_^
🌍 https://www.fabriziomusacchio.com/blog/2023-07-30-wgan_with_direct_wasserstein_distance/
I actually wrote a short introduction to #WassersteinDistance and #OptimalTransport some time ago, if you’re looking for a more intuitive entry point:
🌍 https://www.fabriziomusacchio.com/blog/2023-07-23-wasserstein_distance/
📐📚New study on #WassersteinDistance: Bonet et al. study #geodesic rays in #Wasserstein space and derive conditions for their existence. They show that #Busemann functions can be computed via #OT, with closed-form solutions for 1D and Gaussian cases. This enables efficient sliced distances for labeled datasets, closely matching classical metrics at lower cost and supporting dataset “flows” for #TransferLearning.
📐 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.
Fabrizio Musacchio
Reddit Tech VN Bot
N-gated Hacker News
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Ben Cardoen
Fabrizio Musacchio