  Recently there has been significant activity in developing algorithms with
provable guarantees for topic modeling. In standard topic models, a topic (such
as sports, business, or politics) is viewed as a probability distribution $\vec
a_i$ over words, and a document is generated by first selecting a mixture $\vec
w$ over topics, and then generating words i.i.d. from the associated mixture
$A{\vec w}$. Given a large collection of such documents, the goal is to recover
the topic vectors and then to correctly classify new documents according to
their topic mixture.
  In this work we consider a broad generalization of this framework in which
words are no longer assumed to be drawn i.i.d. and instead a topic is a complex
distribution over sequences of paragraphs. Since one could not hope to even
represent such a distribution in general (even if paragraphs are given using
some natural feature representation), we aim instead to directly learn a
document classifier. That is, we aim to learn a predictor that given a new
document, accurately predicts its topic mixture, without learning the
distributions explicitly. We present several natural conditions under which one
can do this efficiently and discuss issues such as noise tolerance and sample
complexity in this model. More generally, our model can be viewed as a
generalization of the multi-view or co-training setting in machine learning.
