So what are the advantages of ANN classifiers over the AdaBoost or Boosting algorithm?
from comments, by request:
In terms of running time, performance, something else? In terms of error rates, these two methods are hard to compare theoretically. AdaBoost's performance depends on the choice of a base learner and whether the weak learning assumption is satisfied in the particular instance. ANN will work for some problems/distributions but not others. I think this question would be better answered in a different forum.
As Reyzin said, they can be compared from different perspectives.I like all the theoretical beautiful stuff about boosting methods, their convergence guarantees and their bound on generalization error. In reality however, you have to remember boosting methods are meta-algorithms while ANN is a learning method, i.e., ANN can be used as a weak learner in a boosting method.
Lets assume you mean comparing the accuracy of the Adaboost with decision tree as a weak learn and deep neural networks which are the current buzzwords.
DNNs are able to learn very complex structures. Adaboost with decision trees CAN'T. Adaboost can learn perfect classifier when some or all variables are categorical. DNNs CAN'T.
Adaboost are great when we have relative small size datasets. Work very well with most of the medical related datasets and work OK with images.
DNNs and particularly convolutional neural nets (CNNs) are perfect for images and work poorly with small size datasets need a lot of computation power (If you want to train a good model they should be run on GPU) and sometimes can surprise you by the amazing accuracy that they may return.