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We apply machine learning in the form of a nearest neighbor instance-basedalgorithm (NN) to generate full photometric redshift probability densityfunctions (PDFs) for objects in the Fifth Data Release of the Sloan Digital SkySurvey (SDSS DR5). We use a conceptually simple but novel application of NN togenerate the PDFs - perturbing the object colors by their measurement error -and using the resulting instances of nearest neighbor distributions to generatenumerous individual redshifts. When the redshifts are compared to existing SDSSspectroscopic data, we find that the mean value of each PDF has a dispersionbetween the photometric and spectroscopic redshift consistent with othermachine learning techniques, being sigma = 0.0207 +/- 0.0001 for main samplegalaxies to r < 17.77 mag, sigma = 0.0243 +/- 0.0002 for luminous red galaxiesto r < ~19.2 mag, and sigma = 0.343 +/- 0.005 for quasars to i < 20.3 mag. ThePDFs allow the selection of subsets with improved statistics. For quasars, theimprovement is dramatic: for those with a single peak in their probabilitydistribution, the dispersion is reduced from 0.343 to sigma = 0.117 +/- 0.010,and the photometric redshift is within 0.3 of the spectroscopic redshift for99.3 +/- 0.1% of the objects. Thus, for this optical quasar sample, we canvirtually eliminate 'catastrophic' photometric redshift estimates. In additionto the SDSS sample, we incorporate ultraviolet photometry from the Third DataRelease of the Galaxy Evolution Explorer All-Sky Imaging Survey (GALEX AIS GR3)to create PDFs for objects seen in both surveys. For quasars, the increasedcoverage of the observed frame UV of the SED results in significant improvementover the full SDSS sample, with sigma = 0.234 +/- 0.010. We demonstrate thatthis improvement is genuine. [Abridged]

Robust Machine Learning Applied to Astronomical Datasets III: Probabilistic Photometric Redshifts for Galaxies and Quasars in the SDSS and GALEX