Margin bounds in machine learning theory apply to arbitrary mixture-of-experts hypotheses of the form:
h(x) = sign(sum(ai * gi(x)))
where gi(x) predicts either 1 or -1.
I will discuss the original margin bound by Schapire, Freund, Bartlett, and Lee:
Robert E. Schapire, Yoav Freund, Peter Bartlett and Wee Sun Lee. Boosting the margin: A new explanation for the effectiveness of voting methods. The Annals of Statistics, 26(5):1651-1686, 1998.
Then I will present some new work which functionally tightens the bound and has implications for mixture-of-expert learning algorithm design.