  Mean plane measurements of the Kuiper Belt from observational data are of
interest for their potential to test dynamical models of the solar system.
Recent measurements have yielded inconsistent results. Here we report a
measurement of the Kuiper Belt's mean plane with a sample size more than twice
as large as in previous measurements. The sample of interest is the
non-resonant Kuiper belt objects, which we identify by using machine learning
on the observed Kuiper Belt population whose orbits are well-determined. We
estimate the measurement error with a Monte Carlo procedure. We find that the
overall mean plane of the non-resonant Kuiper Belt (semimajor axis range 35-150
au) and also that of the classical Kuiper Belt (semimajor axis range 42-48 au)
are both close to (within about 0.7 degrees) but distinguishable from the
invariable plane of the solar system to greater than 99.7% confidence. When
binning the sample into smaller semimajor axis bins, we find the measured mean
plane mostly consistent with both the invariable plane and the theoretically
expected Laplace surface forced by the known planets. Statistically significant
discrepancies are found only in the semimajor axis ranges 40.3-42 au and 45-50
au; these ranges are in proximity to a secular resonance and Neptune's 2:1 mean
motion resonance where the theory for the Laplace surface is likely to be
inaccurate. These results do not support a previously reported anomalous warp
at semimajor axes above 50 au.
