Predicting which apps users may be interested in
Broadly speaking, what you want is a recommender system. If you consider only the user-app association data (app installs, likes, etc.), and no user or app metadata, then you should look at collaborative filtering.

More specifically, a simpler technique you can consider is item-similarity based recommendation (users who install app A, also install app B). A slightly more complex method involves factorization of the partial user-app association matrix and then inferring missing points in the matrix. This paper describes one such factorization technique used in the Netflix Prize movie recommendation challenge.