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 an d frequently measuring a complete TM in a large-scale network is costly and difficult to perform due to routers limited capaci ties. In this paper we introduce and evaluate a new method to estima te a TM from easily available link load measurements. The metho d uses a novel statistical learning technique to unveil the re lation between links traffic volume and origin-destination flows vo lume. 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 particu lar behavior. Using real data from an operational backbone netw ork, we compare this new method to the most well known and accepted TM estimation techniques, including in the evalua tion some more accurate and up-to-date methods developed in rece nt works. Results show that current TM estimation techniques can still be improved