Max-margin structured output learning in L1 norm space
Sandor Szedmak, Craig Saunders, Yizhao Ni and Juho Rousu
(2009) Technical Report. Sandor Szedmak, Southampton, UK.

## Abstract

We study a structured output learning setting where both the sample size and dimensions of the feature vectors of both the input and output are very large (possibly infinite in the latter case), but the input and output feature representations are non-negative and very sparse (i.e. the number of non-zero components is finite and their proportion to the dimension is close to zero). Such situations are encountered in real-world problems such as statistical machine translation. We show that in this setting structured output learning can be efficiently implemented. The solution relies on maximum margin learning of the linear relations between the inputs and outputs in an $L_1$ norm space. This learning problem can be formulated by imposing $L_{\infty}$ norm regularisation on the linear transformation expressing the relations.