  After decades of progress and effort, obtaining a phase diagram for a
strongly-correlated topological system still remains a challenge. Although in
principle one could turn to Wilson loops and long-range entanglement,
evaluating these non-local observables at many points in phase space can be
prohibitively costly. With growing excitement over topological quantum
computation comes the need for an efficient approach for obtaining topological
phase diagrams. Here we turn to machine learning using quantum loop topography
(QLT), a notion we have recently introduced. Specifically, we propose a
construction of QLT that is sensitive to quasi-particle statistics. We then use
mutual statistics between the spinons and visons to detect a $\mathbb{Z}_{2}$
quantum spin liquid in a multi-parameter phase space. We successfully obtain
the quantum phase boundary between the topological and trivial phases using a
simple feed-forward neural network. Furthermore, we demonstrate advantages of
our approach for the evaluation of phase diagrams relating to speed and
storage. Such statistics-based machine learning of topological phases opens new
efficient routes to studying topological phase diagrams in strongly correlated
systems.
