  Multi-particle interference is an essential ingredient for fundamental
quantum mechanics phenomena and for quantum information processing to provide a
computational advantage, as recently emphasized by Boson Sampling experiments.
Hence, developing a reliable and efficient technique to witness its presence is
pivotal towards the practical implementation of quantum technologies. Here we
experimentally identify genuine many-body quantum interference via a recent
efficient protocol, which exploits statistical signatures at the output of a
multimode quantum device. We successfully apply the test to validate
three-photon experiments in an integrated photonic circuit, providing an
extensive analysis on the resources required to perform it. Moreover, drawing
upon established techniques of machine learning, we show how such tools help to
identify the - a priori unknown - optimal features to witness these signatures.
Our results provide evidence on the efficacy and feasibility of the method,
paving the way for its adoption in large-scale implementations.
