  Astronomical observations are affected by several kinds of noise, each with
its own causal source; there is photon noise, stochastic source variability,
and residuals coming from imperfect calibration of the detector or telescope.
The precision of NASA Kepler photometry for exoplanet science---the most
precise photometric measurements of stars ever made---appears to be limited by
unknown or untracked variations in spacecraft pointing and temperature, and
unmodeled stellar variability. Here we present the Causal Pixel Model (CPM) for
Kepler data, a data-driven model intended to capture variability but preserve
transit signals. The CPM works at the pixel level so that it can capture very
fine-grained information about the variation of the spacecraft. The CPM
predicts each target pixel value from a large number of pixels of other stars
sharing the instrument variabilities while not containing any information on
possible transits in the target star. In addition, we use the target star's
future and past (auto-regression). By appropriately separating, for each data
point, the data into training and test sets, we ensure that information about
any transit will be perfectly isolated from the model. The method has four
hyper-parameters (the number of predictor stars, the auto-regressive window
size, and two L2-regularization amplitudes for model components), which we set
by cross-validation. We determine a generic set of hyper-parameters that works
well for most of the stars and apply the method to a corresponding set of
target stars. We find that we can consistently outperform (for the purposes of
exoplanet detection) the Kepler Pre-search Data Conditioning (PDC) method for
exoplanet discovery.
