arXiv:2405.15379v3 Announce Type: replace-cross Abstract: In this paper, we study the problem of sampling from log-concave distributions supported on convex and compact sets, with a particular focus on the randomized midpoint discretization of both overdamped and kinetic Langevin diffusions in constrained domains. We revisit the proximal framework for handling constraints through projection operators and develop a more general formulation that encompasses Euclidean, Bregman, and Gauge projections. The resulting smooth approximation allows a unified and tractable analysis of Langevin algorithms
This paper leverages recent advancements in computational methods and theoretical understanding of statistical sampling, building on existing challenges in efficient log-concave distribution sampling.
Improved sampling methods for log-concave distributions are crucial for advancing machine learning algorithms, particularly in areas like Bayesian inference, optimization, and statistical modeling, which underpin many AI applications.
The proposed randomized midpoint method offers a more unified and tractable analytical framework for constrained Langevin algorithms, potentially leading to more efficient and robust sampling in complex high-dimensional spaces.
- · AI researchers
- · Machine learning developers
- · Statistical modeling
- · Optimization software
- · Inefficient sampling methods
- · Algorithms with high computational cost
More accurate and faster training of complex AI models.
Reduced computational resource requirements for certain AI tasks, democratizing access to advanced AI capabilities.
Acceleration of scientific discovery through more robust statistical analysis and inference tools.
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Read at arXiv cs.LG