Lmst

https://kantorovich.org/
As the site itself says "The Kantorovich Initiative is dedicated towards research and dissemination of modern mathematics of optimal transport towards a wide audience of researchers, students, industry, policy makers and the general public."
#optimaltransport #shape #geometry #mathematics

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

Wasserstein approximation for differently shifted target distributions. The approximation becomes less accurate for increasing shifts (compared to the Wasserstein distance calculated with scipy).

Wasserstein approximation for different standard deviations of the target set. Also here, the approximation becomes less accurate for increasing standard deviations (compared to the Wasserstein distance calculated with scipy).

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/

Optimal transport plan calculated with Sinkhorn algorithm.

Optimal transport plan calculated with linear programming.

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 Cost matrix C and Optimal transport matrix G for two example distributions.

#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)

Figure 3.3 from mentioned thesis; shown is a 2D labyrinth and snapshots how a Gaussian blob moves optimally from a start to an end position. During transport, the blob changes its shape and takes short paths around corners.

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

#Introdiction : I'm a mathematician moving towards data science topics, based in Chile. Some interests:
#geometry #datageometry #discretegeometry #materialscience
#hyperbolicneuralnetwork
#GraphNeuralNetwork #GNNs
#topology #TDA #metricspaces
#equivariantneuralnetwork #enns #convolutionalneuralnetwork #networkscience
#computationalchemistry #dft #pinns
#optimaltransport
#learningTheory #generalization
#expressivity
#marinescience #biodiversity #oceanscience
#phylogenetics

The first is Éric Daoud, who defended on Monday.

His dissertation is titled "Geographic and socio-demographic disparities in oncology care pathways" and was supervised by Fabien Reyal and Marc Lelarge. Éric was a member of a working group we had on #machineLearning and #electronicHealthRecords until I was sick. See his preprints here: https://edaoud.com/research/ Interesting applications of #optimalTransport inside!

2/3

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.

@johnurbanik oof, forgot to tag #ML #embeddings #optimaltransport #newtothis

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

#OptimalTransport

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