This paper introduces a novel method for optimizing functions on product spaces of simplices, which are relevant to tasks like learning probability distributions and functional data registration. The approach involves reparameterizing the product simplex into a smooth manifold, transforming the unconstrained optimization problem. This reparameterization maps second-order KKT points on the manifold to weak second-order KKT points on the original simplex, enabling a Riemannian Gradient Descent algorithm that outperforms projected gradient descent and offers a more accurate representation of function shapes. AI
IMPACT Introduces a new optimization technique applicable to machine learning tasks like probabilistic tensor decomposition and functional data registration.
RANK_REASON The item is an academic paper submitted to arXiv. [lever_c_demoted from research: ic=1 ai=1.0]
- arXiv
- Karush–Kuhn–Tucker conditions
- Projected Gradient Descent
- Riemannian gradient descent methods for graph-regularized matrix completion
- Square Root Velocity Function
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