The maximum likelihood neural network as a statistical classification model

David Faraggi, Richard Simon

Research output: Contribution to journalArticlepeer-review


Neural networks have received considerable attention in recent years. This development has been pursued primarily by non-statisticians. Consequently many statistical tools and concepts have not been utilized in this development and great claims for neural networks have sometimes been made without comparisons to standard statistical procedures. In this paper we utilize the input-output relationship associated with a simple feed-forward neural network as the basis for a non-linear multivariate classifier. A statistical model for the data is defined based on a logistic likelihood function. Neural network parameters are estimated using the method of maximum likelihood instead of the back-propagation technique often used in the neural network literature. An extension for the multinomial case is presented. These maximum likelihood based models can be compared using readily available techniques such as the likelihood ratio test and the Akaike criterion (1973). We provide empirical comparisons of this network approach with standard logistic regression for both the binomial and multinomial cases.

Original languageEnglish
Pages (from-to)93-104
Number of pages12
JournalJournal of Statistical Planning and Inference
Issue number1
StatePublished - Jul 1995
Externally publishedYes


  • Classification
  • Feed-forward neural networks
  • Logistic likelihood
  • Maximum likelihood

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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