  State-of-the-art physics experiments require high-resolution, low-noise, and
low-threshold detectors to achieve competitive scientific results. However,
experimental environments invariably introduce sources of noise, such as
electrical interference or microphonics. The sources of this environmental
noise can often be monitored by adding specially designed "auxiliary devices"
(e.g. microphones, accelerometers, seismometers, magnetometers, and antennae).
A model can then be constructed to predict the detector noise based on the
auxiliary device information, which can then be subtracted from the true
detector signal. Here, we present a multivariate noise cancellation algorithm
which can be used in a variety of settings to improve the performance of
detectors using multiple auxiliary devices. To validate this approach, we apply
it to simulated data to remove noise due to electromagnetic interference and
microphonic vibrations. We then employ the algorithm to a cryogenic light
detector in the laboratory and show an improvement in the detector performance.
Finally, we motivate the use of nonlinear terms to better model vibrational
contributions to the noise in thermal detectors. We show a further improvement
in the performance of a particular channel of the CUORE detector when using the
nonlinear algorithm in combination with optimal filtering techniques.
