提出新优化方法，让无似然参数估计更稳定高效。
A Gradient Flow Perspective on Minimum MMD Estimation
- 基于概率测度空间的梯度流思想设计预条件梯度下降法。
- 在非凸条件下实现全局收敛，理论保证更强。
- 适合复杂模型参数估计与假设检验，性能优于传统方法。
最小最大均值差异（MMD）估计已成为一种稳健且无需似然的参数估计方法，替代最大似然估计。尽管实践成功，其优化问题仍缺乏理论理解，现有算法的理论保证依赖于极少成立的凸性假设。本文提出一种预条件梯度下降（PGD）方案，在显式的梯度主导性和投影残差条件下，建立了其渐近全局收敛性。该方法受近期关于MMD梯度流研究启发，是一种定义在概率测度空间上的非参数下降策略。我们提供了大量实证证据，表明该PGD方法在多个挑战性的参数估计和复合假设检验任务中均优于标准梯度下降。
原文摘要 · Abstract (English)
Minimum maximum mean discrepancy (MMD) estimation has emerged as a robust and likelihood-free alternative to maximum likelihood estimation for parameter estimation. Yet, despite its practical success, the associated optimization problem remains poorly understood, with theoretical guarantees for existing algorithms hinging on convexity assumptions that rarely hold in practice. We address this gap by proposing a preconditioned gradient descent (PGD) scheme, establishing its asymptotic \emph{global} convergence under explicit gradient-dominance and projection-residual conditions. Our approach is inspired by recent progress on MMD gradient flows, a nonparametric descent scheme on the space of probability measures. We provide extensive empirical evidence that our PGD scheme outperforms standard gradient descent across a range of challenging parameter estimation and composite hypothesis testing problems.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。