Searches of new phenomena in high-energy physics involve testing for the presence of a signal in a mixture model consisting of a background component and a signal component in a high-dimensional space of particle collision events. Modern particle physics experiments, such as those at the Large Hadron Collider at CERN, rely heavily on classifiers to perform this test. When a reliable model for both the background and the signal is available, the output of a supervised classifier can be used to obtain a powerful test for the presence of a signal. However, many open problems arise when either the signal or the background distributions are not well-known in advance. In this talk, I will present recent progress in these situations. In the first case, where the signal distribution is unknown, a semi-supervised classifier can be used as the basis of the test and I will describe methods for calibration, interpretation and signal strength estimation in this context. In the second case, where the background distribution is unknown, I will describe an approach based on optimal transport, which produces a data-driven background estimate by morphing a closely related signal-free data sample.