Continuously Parameterized Mixture Models
Continuously Parameterized Mixture Models
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发表时间：
2023
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通讯作者：
Christopher M. Bender;Yi Shi;M. Niethammer;Junier B. Oliva
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作者：
Christopher M. Bender;Yi Shi;M. Niethammer;Junier B. Oliva
混合模型是光滑密度的通用近似器，但由于对典型可用模式的限制和初始化的挑战，难以在复杂数据集中使用。我们表明，通过使用学习的常微分方程连续参数化因子分析器的混合物，我们可以提高混合模型的拟合度。一旦训练完成，混合成分就可以被提取出来，神经ODE就可以被丢弃，给我们留下一个有效但资源少的模型。此外，我们还探讨了从一个易于建模的潜在空间提取的归一化流到更复杂的输入空间的训练课程的使用，并表明，顺利的课程有助于稳定和改善结果与不连续参数化。最后，我们引入了一个层次化的模型，使更灵活，更强大的分类和聚类，并显示出对传统的参数化的Gestival的实质性改进。
Mixture models are universal approximators of smooth densities but are difficult to utilize in complicated datasets due to restrictions on typically available modes and challenges with initialiations. We show that by continuously parameterizing a mixture of factor analyzers using a learned ordinary differential equation, we can improve the fit of mixture models over direct methods. Once trained, the mixture components can be extracted and the neural ODE can be discarded, leaving us with an effective, but low-resource model. We additionally explore the use of a training curriculum from an easy-to-model latent space extracted from a normalizing flow to the more complex input space and show that the smooth curriculum helps to stabilize and improve results with and without the continuous parameterization. Finally, we introduce a hierarchical version of the model to enable more flexible, robust classification and clustering, and show substantial improvements against traditional parameterizations of GMMs.