  Predictable Feature Analysis (PFA) (Richthofer, Wiskott, ICMLA 2015) is an
algorithm that performs dimensionality reduction on high dimensional input
signal. It extracts those subsignals that are most predictable according to a
certain prediction model. We refer to these extracted signals as predictable
features.
  In this work we extend the notion of PFA to take supplementary information
into account for improving its predictions. Such information can be a
multidimensional signal like the main input to PFA, but is regarded external.
That means it won't participate in the feature extraction - no features get
extracted or composed of it. Features will be exclusively extracted from the
main input such that they are most predictable based on themselves and the
supplementary information. We refer to this enhanced PFA as PFAx (PFA
extended).
  Even more important than improving prediction quality is to observe the
effect of supplementary information on feature selection. PFAx transparently
provides insight how the supplementary information adds to prediction quality
and whether it is valuable at all. Finally we show how to invert that relation
and can generate the supplementary information such that it would yield a
certain desired outcome of the main signal.
  We apply this to a setting inspired by reinforcement learning and let the
algorithm learn how to control an agent in an environment. With this method it
is feasible to locally optimize the agent's state, i.e. reach a certain goal
that is near enough. We are preparing a follow-up paper that extends this
method such that also global optimization is feasible.
