Infinite Mixture Statistical Model Family

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An Infinite Mixture Statistical Model Family is a mixture model family that can express a infinite component mixture function.



References

2011

  • (Ishiguro, 2011) ⇒ Katsuhiko Ishiguro. (2011). “Complex Data Analysis Using Mixture Models.” In: NTT Technical Review, 9(1).
    • QUOTE: One problem with using mixture models is that we have to determine K in advance. In general, specifying the correct K is very difficult, and using the wrong value of K may degrade model fitting very badly, as seen in the example (Fig. 2(b)). One popular solution is to use an information criterion for choosing the best K, i.e., AIC [4] or BIC [5]. In this case, we prepare several mixture models with different K values and compute the criteria for each learned model.

      Recently, another solution, called the nonparametric Bayes approach, has been developed. It does not demand that K be specified. Instead, the model chooses an appropriate value for K to explain the given data in a probabilistic manner.

      In this article, I introduce the Dirichlet Process Mixture (DPM) model, a nonparametric Bayes extension of usual mixture models. Mathematically, DPM represents a mixture of infinitely many components (Fig. 3(a)[1]).