高斯，为什么总是高斯分布？

最新推荐文章于 2024-01-14 03:13:17 发布

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最新推荐文章于 2024-01-14 03:13:17 发布 · 2.2k 阅读

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高斯混合模型（GMM）常用于数据建模，因为它们是通用函数近似器，能通过增加混合成分数量逼近任何原始分布。即使数据原本并非来自GMM，也能通过GMM进行精确建模。这类似于傅立叶变换原理，可通过不同幅值的高斯分布逼近任意分布。

前段时间的group reading 上，一个senior lecturer发出上述疑问我想不光是她，很多人都有或有过类似的想法。正好research gate上有这样的问答，我觉得解释的很清楚了---尽管很简短

If I have a dataset, how can I prove that this dataset has a nature of Gaussian Mixture Model GMM?

One reason why GMMs are used without asking the question if the data is GMM distributed lies in the fact that a GMM is a universal function approximator. That is, whatever the original distribution of the data was, when allowing a significant number of mixture components, it is expected that the GMM approaches the true distribution.

As Marco Huber said, GMMs are flexible appr