Dirichlet Process Mixture Model
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A Dirichlet Process Mixture Model is an infinite mixture model for a Dirichlet process.
- AKA: DP Mixture.
- Context:
- It can be fitted by a DP Mixture Model Fitting Algorithm.
- …
- Counter-Example(s):
- See: Dirichlet Probability 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]).
- 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.
![[1]](https://www.ntt-review.jp/archive_html/201101/images/ra1_fig03.gif){kind=link}
2007
- (Jara et al., 2007) ⇒ Alejandro Jara, María José García-Zattera, and Emmanuel Lesaffre. (2007). “A Dirichlet Process Mixture Model for the Analysis of Correlated Binary Responses.” In: Computational Statistics & Data Analysis, 51(11). doi:10.1016/j.csda.2006.09.010
2005
2000
- (Neal, 2000) ⇒ Radford M. Neal. (2000). “Markov Chain Sampling Methods for Dirichlet Process Mixture Models.” In: Journal of Computational and Graphical Statistics, 9(2).
- This article reviews Markov chain methods for sampling from the posterior distribution of a Dirichlet process mixture model and presents two new classes of methods.