deletions | additions       diff --git a/Inference_Our_inference_method_is__.md b/Inference_Our_inference_method_is__.md  index fcded99..8e9ec0e 100644  --- a/Inference_Our_inference_method_is__.md  +++ b/Inference_Our_inference_method_is__.md 
...
## #  Inference Our inference method is one of our primary contributions to the state of the art.  ### ##  State of the Art The result of the models above is a probability density. The catch is that unlike with simpler models, the integral representing our density is intractable. One solution makes use of the fact that while intergrating over the whole measure space is difficult, plugging in values and retrieving an (un-normalised) probability is not. We can exploit this property by performing an intelligent random walk over the surface of the density. The idea is that if we walk for long enough, we'll obtain a reasonable representation of the surface. This is the basis for a family of inference methods called Markov-Chain Monte-Carlo (MCMC) sampling.  All current Bayesian TLG formulations use MCMC based inference methods \cite{Ahmed2011, Hong:2011du, Wang2013, Ahmed:2012vh, Li2013}. They are simple to implement and an intuitive method for exploring an unknown density. On the other hand they tend to scale poorly with both data-set size or dimensionality \cite{wainwright2008graphical, Grimmer_2010}. NLP in general tends to have large amounts of sparse high dimensional data. Furthermore TLG is a summarisation task and the value of summarisation grows with the size of the underlying data. Because of this, exploring additional inference methods is an important goal for further research.  ### ##  Contributions Inference in nonparametric Bayesian formulations can largely be divided into sampling and expectation-maximisation (EM) like approaches. The former has been applied to TLG but as of yet no attempt has been made to apply the latter. The work of Wang et al. \cite{Wang2011} and Bryant et al.\cite{Bryant2012} on variational inference is a step in this direction. They develop a variational framework for the hierarchal dirichlet model, a fundamental part of all nonparametric TLG formulations. As such we seek to build on their work and apply it to specifically the TLG case. Our goal is motivated by the excellent performance of variational inference. This is both generally \cite{Grimmer_2010} and specifically; Wang et al.\cite{Wang2011} had excellent performance on a dataset of 400,000 articles, an order of magnitude larger than any sampling-based inference on the TLG problem.