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Practical Identifiability of Finite Mixtures of Multivariate Bernoulli Distributions

Department of Computer Science, University of Sheffield, Sheffield S1 4DP, U.K.

Steve Renals

Department of Computer Science, University of Sheffield, Sheffield S1 4DP, U.K.

The class of finite mixtures of multivariate Bernoulli distributions is known to be nonidentifiable; that is, different values of the mixture parameters can correspond to exactly the same probability distribution. In principle, this would mean that sample estimates using this model would give rise to different interpretations. We give empirical support to the fact that estimation of this class of mixtures can still produce meaningful results in practice, thus lessening the importance of the identifiability problem. We also show that the expectation-maximization algorithm is guaranteed to converge to a proper maximum likelihood estimate, owing to a property of the log-likelihood surface. Experiments with synthetic data sets show that an original generating distribution can be estimated from a sample. Experiments with an electropalatography data set show important structure in the data.