发表机构
The Institute of Statistical Mathematics; The Graduate Institute for Advanced Studies, SOKENDAI; RIKEN（统计数学研究所; 索兰代高级研究院; 理化学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究调整Wang的同方差情形论证，证明有限异方差高斯混合的临界点与模态数量均有限，填补了异方差高斯混合临界点有限性的理论空白。
AI 中文摘要
通过略微调整Wang近期针对同方差（homoscedastic）情形的重要论证，我们证明每个有限异方差（heteroscedastic）高斯混合仅具有限个临界点，故仅具有限个模态。
英文摘要
By slightly adapting Wang's recent important argument for the homoscedastic setting, we prove that every finite heteroscedastic Gaussian mixture has only finitely many critical points, and, consequently, only finitely many modes.
Comments4 pages, no figure
