Infinite Mixture Statistical Model Family

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

• • …
• Example(s):
  • a Gaussian Infinite Mixture Model Family (of Gaussian infinite mixture functions).
  • …
• Counter-Example(s):
  • a Finite Mixture Model Famity.
• See: Dirichlet Process Mixture Model.

---

---

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]).

---