Mixture Model Fitting Task

A Mixture Model Fitting Task is a continuous probability model fitting task that can accept a mixture model family to produce a probabilistic component function.

• AKA: Data-Driven Mixture Modeling.
• Context:
  • It can range from being a Finite Mixture Model Fitting Task to being an Infinite Mixture Model Fitting Task.
  • It can be solved by a Mixture Model Fitting System (that implements a Mixture Model Fitting Algorithm).
• Example(s):
  • Gaussian Mixture Models Fitting.
  • Gaussian Mixture Model Fitting Task.
  • …
• Counter-Example(s):
  • Heuristic Mixture Modeling.
• See: Likelihood Estimation.

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References

1999

• (Figueiredo et al., 1999) ⇒ Málrio A.T. Figueiredo, José M.N. Leitão, and Anil K. Jain. “On Fitting Mixture Models.” In: Energy minimization methods in computer vision and pattern recognition.
  • ABSTRACT: Consider the problem of fitting a finite Gaussian mixture, with an unknown number of components, to observed data. This paper proposes a new minimum description length (MDL) type criterion, termed MMDL(for mixture MDL), to select the number of components of the model. MMDLis based on the identification of an “equivalent sample size”, for each component, which does not coincide with the full sample size. We also introduce an algorithm based on the standard expectationmaximization (EM) approach together with a new agglomerative step, called agglomerative EM (AEM). The experiments here reported have shown that MMDLo utperforms existing criteria of comparable computational cost. The good behavior of AEM, namely its good robustness with respect to initialization, is also illustrated experimentally.

1994

• (Bailey & Elkan, 1994) ⇒ Timothy L. Bailey, and Charles Elkan. (1994). “Fitting a Mixture Model by Expectation Maximization to Discover Motifs in Bipolymers."

1988

• (McLachlan & Basford, 1988) ⇒ Geoffrey J. McLachlan, and Kaye E. Basford. (1988). “Mixture Models: Inference and applications to clustering." Applied Statistics.
  • BOOK OVERVIEW: The book gives a comprehensive account of the theoretical and computational issues for likelihood estimation in a finite mixture framework. Emphasizing the importance of mixture models in cluster analysis, the book shows how this approach to clustering provides a framework for assessing the number of clusters and their effectiveness. It also gives a detailed description of how bootstrap methodology can be used in these clustering problems. Numerous examples involving the statistical analyses of real data sets are presented throughout to demonstrate the various applications of finite mixture models. A FORTRAN listing of computer programs is given in the Appendix for the fitting of normal mixture models to data sets from a variety of experimental designs. It also contains a review of items concerned with the actual fitting of mixture models, such as detection of atypical observations, assessment of model fit, and robust estimation. The contents are the following: 1. General introduction; 2. Mixture models with normal components; 3. Applications of mixture models to two- way data sets; 4. Estimation of mixing proportions; 5. Assessing the performance of the mixture likelihood approach to clustering; 6. Partitioning of treatment means in ANOVA; 7. Mixture likelihood approach to the clustering of three-way data. Over 350 references are given. The book is an invaluable resource for applied and theoretical statisticians, biometricians, engineers in pattern recognition and psychologists

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