arXiv:2310.09149v3 Announce Type: replace-cross Abstract: We study the approximation of probability measures in the Wasserstein-$p$ distance by structured classes of approximators, motivated by applications in imaging, machine learning, and physical measurement under sensor constraints. We obtain three sets of results. First, for measures with densities bounded away from zero on a bounded Lipschitz domain $\Omega$, we prove that any approximation scheme for functions in $\mathrm{L}_p(\Omega)$ transfers, with linear rate, to a corresponding approximation scheme for measures in $\mathrm{W}_p(\Om
This research, published on arXiv, indicates ongoing foundational advancements in machine learning theory, specifically addressing a core problem in approximating complex data distributions.
Improved methods for approximating probability measures directly impact the efficiency and accuracy of AI models, crucial for many applications from imaging to advanced machine learning systems.
This theoretical work suggests better mathematical tools for handling uncertainty and complexity in data, potentially enabling more robust and reliable AI agents and systems.
- · AI researchers
- · Machine learning engineers
- · Companies developing computer vision applications
- · Robotics companies
- · Inefficient AI approximation methods
- · Organizations reliant on older, less accurate data processing techniques
More accurate and efficient AI models in various domains, particularly those involving imaging and sensor data.
Accelerated development of AI agents capable of understanding and interacting with complex real-world environments more effectively.
Enhanced AI capabilities contributing to breakthroughs in scientific discovery and automated systems with higher fidelity and lower error rates.
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Read at arXiv cs.LG