凸聚类是一种很有前途的新方法，聚类的经典问题，结合了强大的性能，在实证研究和严格的理论基础。尽管有这些优点，凸聚类还没有被广泛采用，由于其计算密集的性质和缺乏令人信服的可视化。为了解决这些障碍，我们引入了正则化，这是一种创新技术，用于使用迭代一步近似方案获得正则化路径的高质量估计。我们证明我们的方法与一个新的理论结果，保证全局收敛的近似路径下容易检查的非数据依赖的假设下的精确解。将算法正则化应用到凸聚类中，产生了用于计算聚类解路径的凸聚类算法CARP（Convex Clustering via Acromic Regularization Paths）。在基因组学和文本分析的示例数据集上，CARP提供了比现有方法快100倍的速度，同时获得了比标准方法更精细的近似网格。此外，CARP能够改进聚类解决方案的可视化：CARP返回的精细解决方案网格可用于构建基于凸聚类的树状图，并形成基于现代Web技术的动态路径可视化的基础。我们的方法在开源R包clustRviz中实现，可在https://github.com/DataSlingers/clustRviz上获得。
英文摘要：
Convex clustering is a promising new approach to the classical problem of clustering, combining strong performance in empirical studies with rigorous theoretical foundations. Despite these advantages, convex clustering has not been widely adopted, due to its computationally intensive nature and its lack of compelling visualizations. To address these impediments, we introduce Algorithmic Regularization, an innovative technique for obtaining high-quality estimates of regularization paths using an iterative one-step approximation scheme. We justify our approach with a novel theoretical result, guaranteeing global convergence of the approximate path to the exact solution under easily-checked non-data-dependent assumptions. The application of algorithmic regularization to convex clustering yields the Convex Clustering via Algorithmic Regularization Paths (CARP) algorithm for computing the clustering solution path. On example data sets from genomics and text analysis, CARP delivers over a 100-fold speed-up over existing methods, while attaining a finer approximation grid than standard methods. Furthermore, CARP enables improved visualization of clustering solutions: the fine solution grid returned by CARP can be used to construct a convex clustering-based dendrogram, as well as forming the basis of a dynamic path-wise visualization based on modern web technologies. Our methods are implemented in the open-source R package clustRviz, available at https://github.com/DataSlingers/clustRviz.
On the Algorithmic Bias of Aligning Large Language Models with RLHF: Preference Collapse and Matching Regularization
University of Pennsylvania（宾夕法尼亚大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；National University of Singapore（新加坡国立大学）；Peking University（北京大学）；Joint corresponding authors（联合通讯作者）
University of California, Berkeley（加州大学伯克利分校）；University of Texas, Austin（德克萨斯大学奥斯汀分校）；Cornell Tech（康奈尔科技）；Stanford University（斯坦福大学）；University of Pennsylvania（宾夕法尼亚大学）；Harvard University（哈佛大学）；Inria, Paris（巴黎Inria）
Adaptive multi-penalty regularization based on a generalized Lasso path
Department of Mathematical Sciences, Norwegian University of Science and Technology（挪威科学与技术大学数学科学系）；Section for Computing and Software, Simula Research Laboratory AS（Simula研究实验室计算与软件部门）
Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computation
Department of Statistics Columbia University（统计系 哥伦比亚大学）；Department of Computer Science and Department of Statistics Columbia University（计算机科学系和统计系 哥伦比亚大学）
