Maximum likelihood estimation from fuzzy data using the EM algorithm

Authors:
Thierry Denœux
Affiliations:
UMR CNRS 6599 Heudiasyc, Université de Technologie de Compiègne, BP 20529, F-60205 Compiègne cedex, France
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

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.