Despite a large body of literature and methods devoted to the Traffic Matrix (TM) estimation problem, the inference of traffic flows volume from aggregated data still represents a major issue for network operators. Directly and frequently measuring a complete TM in a large-scale network is costly and difficult to perform due to routers limited capacities. In this paper we introduce and evaluate a new method to estimate a TM from easily available link load measurements. The method uses a novel statistical learning technique to unveil the relation between links traffic volume and origin-destination flows volume. By training a system based on Random Neural Networks, we provide a fast and accurate TM estimation tool that attains proper results without assuming any traffic model or particular behavior. Using real data from an operational backbone network, we compare this new method to the most well known and accepted TM estimation techniques, including in the evaluation some more accurate a...