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.
In @cite_7 a comparable approach to PFA is formulated and PFA can be seen as a generalization of the method presented there. We will refer to that method again in a later section.
@cite_7
2070173743
Abstract : This paper proposes a canonical transformation of a k dimensional stationary autoregressive process. The components of the transformed process are ordered from least predictable to most predictable. The least predictable components are often nearly white noise and the most predictable can be nearly nonstationary. Transformed variables which are white noise can reflect relationships which may be associated with or point to economic or physical laws. A 5-variate example is given.