information criteria for confusion matrices

Question

One can measure goodness of fit of a statistical model using Akaike Information Criterion (AIC), which accounts for goodness of fit and for the number of parameters that were used for model creation. AIC involves calculation of maximized value of likelihood function for that model (L). How can one compute L, given prediction results of a classification model, represented as a confusion matrix?

Answer 1

It is not possible to calculate the AIC from a confusion matrix since it doesn't contain any information about the likelihood. Depending on the model you are using it may be possible to calculate the likelihood or quasi-likelihood and hence the AIC or QIC.

What is the classification problem that you are working on, and what is your model?

In a classification context often other measures are used to do GoF testing. I'd recommend reading through The Elements of Statistical Learning by Hastie, Tibshirani and Friedman to get a good overview of this kind of methodology.

Hope this helps.

Answer 2

Information-Based Evaluation Criterion for Classifier's Performance by Kononenko and Bratko is exactly what I was looking for:

Classification accuracy is usually used as a measure of classification performance. This measure is, however, known to have several defects. A fair evaluation criterion should exclude the influence of the class probabilities which may enable a completely uninformed classifier to trivially achieve high classification accuracy. In this paper a method for evaluating the information score of a classifier''s answers is proposed. It excludes the influence of prior probabilities, deals with various types of imperfect or probabilistic answers and can be used also for comparing the performance in different domains.