  Context. Large, high-dimensional astronomical surveys require efficient data
analysis. Automatic fitting of lightcurve variability and machine learning may
assist in identification of sources including candidate quasars.
  Aims. We aim to classify sources from the Palomar Transient Factory (PTF) as
quasars, stars or galaxies, and to examine model performance using variability
and colours. We determine the added value of variability information as well as
quantifying the performance when colours are not available.
  Methods. We use supervised learning in the form of a histogram-based gradient
boosting classifier to predict spectroscopic SDSS classes using photometry. For
comparison, we create models with structure function variability parameters
only, magnitudes only and using all parameters.
  Results. We achieve highly accurate predictions for 71 million sources with
lightcurves in PTF. The full model correctly identifies 92.49 % of
spectroscopically confirmed quasars from the SDSS with a purity of 95.64 %.
With only variability, the completeness is 34.97 % and the purity is 58.71 %
for quasars. The predictions and probabilities of PTF objects belonging to each
class are made available in a catalogue, VILLAIN-Cat, including magnitudes and
variability parameters.
  Conclusions. We have developed a method for automatic and effective
classification of PTF sources using magnitudes and variability. For similar
supervised models, we recommend using at least 100,000 labeled objects, and we
show how performance scales with data volume.
