  Entanglement not only plays a crucial role in quantum technologies, but is
key to our understanding of quantum correlations in many-body systems. However,
in an experiment, the only way of measuring entanglement in a generic mixed
state is through reconstructive quantum tomography, requiring an exponential
number of measurements in the system size. Here, we propose a machine learning
assisted scheme to measure the entanglement between arbitrary subsystems of
size $N_A$ and $N_B$, with $\mathcal{O}(N_A + N_B)$ measurements, and without
any prior knowledge of the state. The method exploits a neural network to learn
the unknown, non-linear function relating certain measurable moments and the
logarithmic negativity. Our procedure will allow entanglement measurements in a
wide variety of systems, including strongly interacting many body systems in
both equilibrium and non-equilibrium regimes.
