Gints Jekabsons' webpage

Adaptive Basis Function Construction (ABFC)

Adaptive Basis Function Construction (ABFC) is an adaptive regression model building approach that, in contrast to the classical fixed-model approaches and subset selection approaches, does not assume a fixed finite predefined dictionary of basis functions. All the required basis functions are constructed adaptively in a data-driven way using a number of state-transition operators in an infinite state/model space. It may be viewed also as a feature construction approach. Initially, the ABFC was developed specifically for induction of arbitrary complex sparse (sometimes also called partial) polynomial regression models (either linear or logistic) with basis functions of non-negative exponents.

Some of the advantages are:

• no need in predefining the full set of basis functions (or the full polynomial);
• no need in predefining the (maximal) degree of basis functions or models;
• increased flexibility in approximating non-linear behaviours;
• inherent ability to filter-out irrelevant input variables;
• reduced computational requirements comparing to the subset selection approach (polynomial time instead of exponential time with respect to the number of features, required non-linearity, and required model complexity).

Two of the proposed ABFC techniques are:

• Floating Adaptive Basis Function Construction (F-ABFC) - adaptively constructs models using the floating search principle in an infinite state/model space;
• Ensemble of F-ABFC (EF-ABFC) - constructs ensembles of F-ABFC models in order to decrease selection bias and selection instability (variance).

Applications: general regression modelling / regression model building, metamodelling (also called surrogate modelling) etc.

The ABFC methods have been successfully applied for metamodelling of composite material degradation in the Specific Targeted Research Project "Improved Material Exploitation at Safe Design of Composite Airframe Structures by Accurate Simulation of Collapse (COCOMAT)" (2004-2008) co-funded by the European Commission within the 6th Framework Programme, as well as in three research projects co-funded by Latvia Ministry of Education and Science and Riga Technical University.

VariReg software tool includes ABFC methods implemented for regression tasks. A Matlab implementation is also available.

VariClass software tool includes ABFC methods implemented for classification tasks (using Logistic Regression and Iteratively Re-weighted Least Squares, IRLS). A Matlab implementation is also available.