If you want a solid year-long project, find a statistical model you like and figure out how to do inference in it with variational Bayes. If this has been done, change finite parts of the model into infinite ones until you reach novelty or the model is no longer recognizable/tractable. At that point, either try a new model or instead try to make the VB inference online or parallelizable. Maybe target a NIPS-style paper and a ~30-page technical report in addition to whatever your thesis will look like.

And attend a machine learning class, if offered. There's a lot of lore in that field and you'll miss out if you do the read-the-book-work-each-problem thing that is alleged to work in math.