A usual way to model a recommendation system is as a matrix completion problem. There are several matrix completion methods, typically using optimization approaches or collaborative filtering. Most approaches assume that the matrix is either low rank, or that there are a small number of latent variables that encode the full problem. Here, we propose a novel matrix completion algorithm for recommendation systems, without any assumptions on the rank and that is model free, i.e., the entries are not assumed to be a function of some latent variables. Instead, we use a technique akin to information theory. Our method performs hybrid neighborhood-based collaborative filtering using Kolmogorov complexity. It decouples the matrix completion into a vector completion problem for each user. The recommendation for one user is thus independent of the recommendation for other users. This makes the algorithm scalable because the computations are highly parallelizable. Our results are competitive with state-of-the-art approaches on both synthetic and real-world dataset benchmarks.