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Evidential EM (E2M) algorithm

An extension of the Expectation-Maximization (EM) algorithm for parameter estimation in statistical models in the case where data are uncertain and represented as belief functions. The proposed method is based on the maximization of a generalized likelihood criterion, which can be interpreted as a degree of agreement between the statistical model and the uncertain observations. E2M is a variant of the EM algorithm that iteratively maximizes this criterion.

The toolbox provides functions for the following problems:

  • Probability estimation from uncertain data (Bernoulli model);
  • Clustering of uncertain categorical data using the latent class model (with the possibility to use uncertain information on class labels);
  • Clustering of uncertain continuous data using the Gaussian mixture model (with the possibility to use uncertain information on class labels).


  1. T. Denoeux. Maximum likelihood from evidential data: an extension of the EM algorithm. In C. Borgelt et al. (Eds), Combining soft computing and statistical methods in data analysis (Proceedings of SMPS 2010, Oviedo, Spain, September 28 - October 1, 2010), Advances in Intelligent and Soft Computing, pages 181-188, Springer, 2010. pdf
  2. T. Denoeux. Maximum likelihood estimation from Uncertain Data in the Belief Function Framework. IEEE Transactions on Knowledge and Data Engineering, Vol. 25, Issue 1, pages 119-130, 2013. pdf


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