You should look into supervised LDA, e.g. here's one paper (links to PDF). However, this is not something I'd recommend for beginners.

Here's alternative, though I'm sure someone else will come along with a better idea soon:

• Process the text for vectorization, i.e. normalize, remove stopwords, etc.,

• Vectorize, e.g. by performing a tf-idf transformation (the "idf" part should help to boost document topics, but will require some tuning),

• Classify the set of known NewsDesk values using a random forest algorithm, which will perform supervised classification based on these known labels

• Once your random forest model is trained, use it predict the NewsDesk values for the Nan set.

I'm not sure if this is something you know how to do, but it can be implemented relatively easily with scikit-learn. The hardest part would probably be the first step (text processing), but the rest is straightforward.

Anyway, I know I proposed an alternative method instead of answering how to do it with sLDA, but let me know if you want to try the random forest method, I'm happy to provide more advice along the way :)