One parameter is always enough
Year: 2018
Type: article
Abstract: We construct an elementary equation fθ(x) with a single real valued parameter θ ∈ [0, 1] that, as θ varies, is capable of fitting any scatter plot on any number of points to within a fixed precision. Specifically, given ϵ > 0, we may construct fθ so that for any collection of ordered pairs {(xj,yj)}j=0n with n,xi∈N and yi ∈ (0, 1), there exists a θ ∈ [0, 1] giving |fθ(xj) − yj| < ϵ for all j simultaneously. To achieve this, we apply results about the logistic map, an iterated map in dynamical systems theory that can be solved exactly. The existence of an equation fθ with this property highlights that “parameter counting” fails as a measure of model complexity when the class of models under consideration is only slightly broad.
Source: AIP Advances
DOI: 10.1063/1.5031956
Author: Steven T. Piantadosi
Institution: University of California, Berkeley
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,350
OpenAlex ID: W2894313147