固定支撑双熵正则化Wasserstein重心的牛顿法
Newton Method for Fixed-Support Doubly Entropic Wasserstein Barycenter
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中文总结 AI 辅助
针对固定支撑双熵正则化Wasserstein重心问题，提出精确牛顿法及稀疏变体，推导梯度与海森显式式，建立理论结果，实验显示稀疏牛顿法收敛更快。
中文摘要 AI 辅助
我们研究固定支撑双正则化Wasserstein重心问题，利用熵最优运输的半对偶形式，将问题重新表述为对偶变量中的光滑无约束凸优化问题。随后推导梯度和海森矩阵的显式表达式，开发用于高精度重心计算的精确牛顿法；为提升可扩展性，提出稀疏牛顿变体，通过稀疏化运输概率矩阵降低海森-向量乘积的成本。我们为所提方法建立理论结果，包括海森近似界和收敛性结果。在合成与真实数据集上的实验表明，稀疏牛顿法收敛速度快于
英文摘要
We study the fixed-support doubly regularized Wasserstein barycenter problem. Using the semi-dual formulation of entropic optimal transport, we reformulate the problem as a smooth, unconstrained, convex optimization problem in the dual variables. We then derive explicit expressions for the gradient and Hessian and develop an exact Newton method for high-accuracy barycenter computation. To improve scalability, we propose a sparse Newton variant that sparsifies the transport probability matrices, thereby reducing the cost of Hessian-vector products. We establish theoretical results for the proposed methods, including Hessian approximation bounds and convergence results. Experiments on synthetic and real datasets show that the sparse Newton method converges faster than
