Valiant is not talking specifically about AdaBoost, although AdaBoost was the first of these algorithms and is well known due to wide proliferation. See this which succinctly describes the differences of some of the different boosters out there. In particular the linked paper by Philip Long at Google is really nice for showing the limitations of boosters and also understanding the fact that boosters are really nothing more than a specialized gradient descent if you recast them in the right way.
I'm not sure boosting is the most powerful general learning method now known - the support vector machine seems more powerful
This is not what is meant here. SVM is a classification rule itself, whereas boosting is a metarule that operates on classification rules themselves and attempts to make coherent use of multiple decision rules each with different degrees of confidence and error. It makes no sense to compare the usefulness of SVMs to the usefulness of boosting, boosting operates on SVMs. To boot, generalized kernel learning methods, sparse dictionary coding, bag-of-words, and Reproducing Kernel Hilbert Space methods all have many cases where they are vastly superior to SVM. For that matter, even simpler methods like Fisher Linear Discriminant can outperform SVM in a lot of practical cases. And SVM lacks much extension to fully unsupervised learning.
I think Valiant, whose office sits down the hall from my adviser's and who I have frequent conversations with, is on the money with this stuff.
...It makes no sense to compare the usefulness of SVMs to the usefulness of boosting If an SVM outperforms a boosted-whatever, then it does make sense to compare them.
boosting operates on SVMs Except that in practice no one uses SVMs as the base learners for boosting (as far as I know). I don't think it would work very well, since basic SVMs are linear models, and adding multiple linear models is useless. Boosting is usually done with decision trees or decision stumps.
bag-of-words That is a feature representation, and it has little to do with the learning me
http://cacm.acm.org/magazines/2011/6/108655-qa-a-lifelong-learner/fulltext
Wow, this is quite interesting. What are your thoughts?