Next generation 5G cellular networks are envisioned to accommodate an unprecedented massive amount of Internet of things (IoT) and user devices while providing high aggregate multi-user sum rates and low latencies. To this end, cloud radio access networks (CRAN), which operate at short radio frames and coordinate dense sets of spatially distributed radio heads, have been proposed. However, coordination of spatially and temporally denser resources for larger sets of user population implies considerable resource allocation complexity and significant system signalling overhead when associated with channel state information (CSI)-based resource allocation (RA) schemes. In this paper, we propose a novel solution that utilizes random forests as supervised machine learning approach to determine the resource allocation in multi-antenna CRAN systems based primarily on the position information of user terminals. Our simulation studies show that the proposed learning based RA scheme performs comparably to a CSI-based scheme in terms of spectral efficiency and is a promising approach to master the complexity in future cellular networks. When taking the system overhead into account, the proposed learning-based RA scheme, which utilizes position information, outperforms legacy CSI-based scheme by up to 100%. The most important factor influencing the performance of the proposed learning-based RA scheme is antenna orientation randomness and position inaccuracies. While the proposed random forests scheme is robust against position inaccuracies and changes in the propagation scenario, we complement our scheme with three approaches that restore most of the original performance when facing random antenna orientations of the user terminal.