Results on universal approximation for learners other than ANNs

I have an applied machine-learning and statistics background, and when I read the Universal approximation theorem, which (in the context of the learning theory of ANNs - Artificial Neural Networks) states (Wikipedia):

"the standard multilayer feed-forward network with a single hidden layer that contains finite number of hidden neurons, and with arbitrary activation function are universal approximators on a compact subset of $R^n$. "

I wondered if there are any similar results (in terms of approximation power) for other types of learners (e.g. decision trees, boosting methods, SVMs, etc.).

This leads me to a second but related question: Is this a topic that is formally studied in TCS? If so, are there any good texts for somebody with an applied background?

Thanks

• Did mean for "ANN" to stand for "Acyclic Neural Network" or something? From my understanding, "ANN" often stands for "Approximate Nearest Neighbor," so this title might be confusing. – Lev Reyzin Jan 30 '11 at 23:59
• @Lev: I think it stands for Artificial Neural Network. – M.S. Dousti Jan 31 '11 at 0:42
• oh I see - that abbreviates to ANN too. Shows how much I know... – Lev Reyzin Jan 31 '11 at 0:58