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/

#OptimalTransport #MachineLearning

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/

#OptimalTransport

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/

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/

Our Pick of the week: Phuong-Hang Le et al., "Pre-training for Speech Translation: CTC Meets Optimal Transport"
by @mgaido91

:arxiv: https://arxiv.org/abs/2301.11716

#NLProc #optimaltransport #CTC #speechtranslation

Hi! #Introduction, now that Ive just shifted servers.
I'm a quantitative scientist working on problems in structural biology and image analysis. I deeply love data! Thus, I straddle math modeling, image analysis, computational methods, and statistics (esp Bayesian). I view myself as an applied mathematician with an inordinate fondness for actual data +craving for good applications.

#mathbio #compchem #StructuralBiology #metalloproteins #optimalTransport #appliedMath
#ImageAnalysis
#HIVresearch

Excited about neural #optimaltransport methods for modeling #singlecell perturbation responses but wondering how to integrate cell birth and death? Frederike Lübeck has the answer for you in the #AI4science workshop @NeuripsConf! Join us in rooms 388 - 390.

Joint work with Frederike Lübeck, Gabriele Gut, Jacobo Sarabia del Castillo, Lucas Pelkmans, David Alvarez Melis, and myself.

Paper: https://arxiv.org/pdf/2209.15621.pdf

Join me at my poster #1035 in Hall J now to hear about conditional neural #optimaltransport with applications in single-cell biology.

#Introduction

I'm a Marie Curie fellow working at Kyoto University and Italian Institute of Technology.
#OPTIMAL project
https://cordis.europa.eu/project/id/101027956

#optimalTransport #AI4science #remoteSensing #culturalHeritage

Today I attended an excellent seminar by Yunan Yang (ETH Zürich) titled "Optimal transport for learning chaotic dynamics via invariant measures" in the #NumericalAnalysis and #ScientificComputing series in Manchester.

Many interesting ideas and a lot to unpack, so I can't do it justice, but here is a summary.

#OptimalTransport #DynamicalSystems #ParameterIdentification #InverseProblems

Klatt, M., Munk, A. & Zemel, Y. Limit laws for empirical optimal solutions in random linear programs. Ann Oper Res 315, 251–278 (2022).

https://doi.org/10.1007/s10479-022-04698-0

#article #ScientificArticle #LimitLaw #OptimalTransport #LinearProgramming #mathematics

Hundrieser, S., Klatt, M., Munk, A. (2022). The Statistics of Circular Optimal Transport. In: SenGupta, A., Arnold, B.C. (eds) Directional Statistics for Innovative Applications. Forum for Interdisciplinary Mathematics. Springer, Singapore.

https://doi.org/10.1007/978-981-19-1044-9_4

#article #ScientificArticle #OptimalTransport #CentralLimitTheorem #clt #VonMisesDistribution #mathematics #InterdisciplinaryMathematics