Optimal Transport for Gaussian Mixture Models
Optimal Transport for Gaussian Mixture Models
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DOI：
10.1109/access.2018.2889838
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发表时间：
2017-10
期刊：
影响因子：
3.9
通讯作者：
Yongxin Chen;T. Georgiou;A. Tannenbaum
中科院分区：
文献类型：
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作者：
Yongxin Chen;T. Georgiou;A. Tannenbaum
我们在高斯混合模型空间上引入一个最优质量传输框架。这些模型在统计推断中被广泛使用。具体而言，我们将高斯混合模型视为配备瓦瑟斯坦度量的概率密度的子流形。由最优传输诱导的拓扑是非常理想且自然的，因为与总变差和其他度量不同，瓦瑟斯坦度量是弱连续的（即，收敛等同于矩的收敛）。因此，我们的方法为比较、插值和平均高斯混合模型提供了自然的方式。此外，该方法具有较低的计算复杂度。我们讨论了该框架的不同方面，并给出示例用于说明目的。
We introduce an optimal mass transport framework on the space of Gaussian mixture models. These models are widely used in statistical inference. Specifically, we treat the Gaussian mixture models as a submanifold of probability densities equipped with the Wasserstein metric. The topology induced by optimal transport is highly desirable and natural because, in contrast to total variation and other metrics, the Wasserstein metric is weakly continuous (i.e., convergence is equivalent to the convergence of moments). Thus, our approach provides natural ways to compare, interpolate, and average Gaussian mixture models. Moreover, the approach has low computational complexity. Different aspects of the framework are discussed, and examples are presented for illustration purposes.