  Topic models, such as Latent Dirichlet Allocation (LDA), posit that documents
are drawn from admixtures of distributions over words, known as topics. The
inference problem of recovering topics from admixtures, is NP-hard. Assuming
separability, a strong assumption, [4] gave the first provable algorithm for
inference. For LDA model, [6] gave a provable algorithm using tensor-methods.
But [4,6] do not learn topic vectors with bounded $l_1$ error (a natural
measure for probability vectors). Our aim is to develop a model which makes
intuitive and empirically supported assumptions and to design an algorithm with
natural, simple components such as SVD, which provably solves the inference
problem for the model with bounded $l_1$ error. A topic in LDA and other models
is essentially characterized by a group of co-occurring words. Motivated by
this, we introduce topic specific Catchwords, group of words which occur with
strictly greater frequency in a topic than any other topic individually and are
required to have high frequency together rather than individually. A major
contribution of the paper is to show that under this more realistic assumption,
which is empirically verified on real corpora, a singular value decomposition
(SVD) based algorithm with a crucial pre-processing step of thresholding, can
provably recover the topics from a collection of documents drawn from Dominant
admixtures. Dominant admixtures are convex combination of distributions in
which one distribution has a significantly higher contribution than others.
Apart from the simplicity of the algorithm, the sample complexity has near
optimal dependence on $w_0$, the lowest probability that a topic is dominant,
and is better than [4]. Empirical evidence shows that on several real world
corpora, both Catchwords and Dominant admixture assumptions hold and the
proposed algorithm substantially outperforms the state of the art [5].
