  A central goal in experimental high energy physics is to detect new physics
signals that are not explained by known physics. In this paper, we aim to
search for new signals that appear as deviations from known Standard Model
physics in high-dimensional particle physics data. To do this, we determine
whether there is any statistically significant difference between the
distribution of Standard Model background samples and the distribution of the
experimental observations, which are a mixture of the background and a
potential new signal. Traditionally, one also assumes access to a sample from a
model for the hypothesized signal distribution. Here we instead investigate a
model-independent method that does not make any assumptions about the signal
and uses a semi-supervised classifier to detect the presence of the signal in
the experimental data. We construct three test statistics using the classifier:
an estimated likelihood ratio test (LRT) statistic, a test based on the area
under the ROC curve (AUC), and a test based on the misclassification error
(MCE). Additionally, we propose a method for estimating the signal strength
parameter and explore active subspace methods to interpret the proposed
semi-supervised classifier in order to understand the properties of the
detected signal. We also propose a Score test statistic that can be used in the
model-dependent setting. We investigate the performance of the methods on a
simulated data set related to the search for the Higgs boson at the Large
Hadron Collider at CERN. We demonstrate that the semi-supervised tests have
power competitive with the classical supervised methods for a well-specified
signal, but much higher power for an unexpected signal which might be entirely
missed by the supervised tests.
