Gaussian Mixture Model Family

A Gaussian Mixture Model Family is a mixture model family of the form [math]\displaystyle{ p(\mathbf{x}) = \sum_{k=1}^K \pi_k N(\mu_k,\Sigma_k) }[/math], where [math]\displaystyle{ \pi_k }[/math] is the probability that a sample is drawn from kth mixture component. Note that [math]\displaystyle{ \sum_{k=1}^K \pi_k = 1 }[/math] and [math]\displaystyle{ \pi_k \gt 0 }[/math].

• Context:
  • It can be instantiated in a Gaussian Mixture Function.
  • It can range from being a Univariate Gaussian Mixture Model Family to being a Multivariate Gaussian Mixture Model Family.
  • It can range from being a Finite Gaussian Mixture Model Family to being an Infinite Gaussian Mixture Model Family.
  • It can be instantiated in a Gaussian Mixture Model.
  • It can be an input to a Gaussian Mixture Model Fitting Task.
  • …
• Counter-Example(s):
  • a Poisson Mixture Model Family.
• See: Generative Statistical Model, Gaussian Density Function, EM Algorithm.

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References

2013

• (Yu et al., 2013) ⇒ Dong Yu, Michael L. Seltzer, Jinyu Li, Jui-Ting Huang, and Frank Seide. (2013). “Feature Learning in Deep Neural Networks-studies on Speech Recognition Tasks.” arXiv preprint arXiv:1301.3605
  • ABSTRACT: Recent studies have shown that deep neural networks (DNNs) perform significantly better than shallow networks and Gaussian mixture models (GMMs) on large vocabulary speech recognition tasks.

2009

• http://www.ics.uci.edu/~smyth/courses/ics274/notes4.pdf
• (Reynolds, 2009) ⇒ Douglas Reynolds. (2009). “Gaussian Mixture Models.” In: Encyclopedia of Biometrics.

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