The VC dimension for mixtures of binary classifiers.
The mixtures-of-experts (ME) methodology provides a tool of classification when experts of logistic regression models or Bernoulli models are mixed according to a set of local weights. We show that the Vapnik-Chervonenkis dimension of the ME architecture is bounded below by the number of experts m and above by O(m4s2), where s is the dimension of the input. For mixtures of Bernoulli experts with a scalar input, we show that the lower bound m is attained, in which case we obtain the exact result that the VC dimension is equal to the number of experts.
Department of Statistics, Northwestern University, Evanston, IL 60208, USA.
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D005103:Expert Systems; D007858:Learning; D016015:Logistic Models; D016571:Neural Networks, Computer