Adaptive Basis Function Construction: An Approach for Adaptive Building of Sparse Polynomial Regression Models

摘要: The task of learning useful models from available data is common in virtually all fields science, engineering, and finance. goal the to estimate unknown (input, output) dependency (or model) training (consisting a finite number samples) with good prediction (generalization) capabilities for future (test) (Cherkassky & Mulier, 2007; Hastie et al., 2003). One specific tasks regression – estimating an real-valued function. process model also called modelling or building. Many practical methods use basis function representation these are dictionary (Friedman, 1994; Cherkassky 2003), where particular type chosen functions constitutes “dictionary”. Further distinction then made between non-adaptive adaptive (also flexible) methods. most widely used form expansions polynomial fixed degree. If always includes (predetermined) set (i.e. they not adapted data), method considered Using however themselves (by employing some kind search mechanism). This restriction degree removed model’s now becomes another parameter fit. Adaptive very wide candidate can, principle, approximate any continuous pre-specified accuracy. known as universal approximation property (Kolmogorov Fomin, 1975, 2007). However, increase leads exponential growth With data, along parameters (coefficients) quickly exceeds samples, making estimation impossible. Additionally should be overly 8