The search for fast optical transients, such as the expected electromagnetic counterparts to binary neutron star mergers, is riddled with false positives ranging from asteroids to stellar flares. While moving objects are readily rejected via image pairs separated by $sim$1 hr, stellar flares represent a challenging foreground that significantly outnumber rapidly-evolving explosions. Identifying stellar sources close to and fainter than the transient detection limit can eliminate these false positives. Here, we present a method to reliably identify stars in deep co-adds of Palomar Transient Factory (PTF) imaging. Our machine-learning methodology utilizes the random forest (RF) algorithm, which is trained using $> 3times{10}^6$ sources with Sloan Digital Sky Survey (SDSS) spectra. When evaluated on an independent test set, the PTF RF model outperforms the SExtractor star classifier by $sim$4%. For faint sources ($rge{21}$ mag), which dominate the field population, the PTF RF model produces a $sim$19% improvement over SExtractor. To avoid false negatives in the PTF transient-candidate stream, we adopt a conservative stellar classification threshold, corresponding to a galaxy misclassification rate = 0.005. Ultimately, $sim$$1.70times{10}^8$ objects are included in our PTF point-source catalog, of which only $sim$$10^6$ are expected to be galaxies. We demonstrate that the PTF RF catalog reveals transients that otherwise would have been missed. To leverage its superior image quality, we additionally create an SDSS point-source catalog, which is also tuned to have a galaxy misclassification rate = 0.005. These catalogs have been incorporated into the PTF real-time pipelines to automatically reject stellar sources as non-extragalactic transients.
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