Supplementary materials to “ Anticipating changes : Adaptation and extrapolation in category learning ”

Footnote 4 in the paper presents an equation that indicates that a simple proportional updating rule corresponds to an exponential filtering scheme. In this first section, we present the derivation of this equation. This result is not new: it is widely known in the statistics literature, but is reproduced here for convenience. The proportional update rule asserts that a prototype previously located at μt−1, after observing a new item located at xt is updated as follows: μt = (1− φ)xt + φμt−1 (1)