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Convex Optimization Project.pdf

ConvexOptProject.pdf
Preview of Convex Optimization Project
🔗 Source: benediktpetko.com
📊 Size: 309 KB
📄 Pages: 10 pages
⬇️ Downloads: 73

Summary

The project focuses on equipping the space of histograms with a suitable metric, specifically the Wasserstein metric, and explores the optimal transport approach in machine learning. The Wasserstein metric is defined as the minimum cost of transporting one probability distribution to another, but computing it is computationally infeasible. To address this, the project introduces the Sinkhorn metric, a regularized version of the Wasserstein metric, which is computable with linear complexity. The Sinkhorn distance is defined as the minimum cost of transporting one histogram to another, subject to an upper bound on the KL divergence from the independence table. The project also discusses the dual Sinkhorn divergence and its relationship to the Sinkhorn distance. The goal is to use the Sinkhorn distance as a surrogate for the Wasserstein metric, which can be used in machine learning tasks such as classification and dimensionality reduction.

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Description

The project focuses on equipping the space of histograms with a suitable metric, specifically the Wasserstein metric, and explores the optimal transport...

Technical Information

  • File Format: PDF
  • File Size: 309 KB
  • Pages: 10
  • Language: EN
  • Total Downloads: 73
  • Last Updated: 3 hours ago

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