Maximum likelihood estimation from fuzzy data using the EM algorithm

Thierry Denoeux (1)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

A method is proposed for estimating the parameters in a parametric statistical model when the observations are fuzzy and are assumed to be related to underlying crisp realizations of a random sample. This method is based on maximizing the observed-data likelihood defined as the probability of the fuzzy data. It is shown that the EM algorithm may be used for that purpose, which makes it possible to solve a wide range of statistical problems involving fuzzy data. This approach, called the Fuzzy EM (FEM) method, is illustrated using three classical problems: normal mean and variance estimation from a fuzzy sample, multiple linear regression with crisp inputs and fuzzy outputs, and univariate finite normal mixture estimation from fuzzy data.

Mots clés: Statistics; fuzzy data analysis; estimation; maximum likelihood principle; regression; mixture models

Domaines: Intelligence artificielle [cs.AI]

Thierry Denoeux. Maximum likelihood estimation from fuzzy data using the EM algorithm. Fuzzy Sets and Systems, 2011, 183 (1), pp.72-91. ⟨hal-00654118⟩