Enhanced Weighted Kernel Regression with Prior Knowledge in Solving Small Sample Problems

In many real-world problems only very few samples are available and sometimes non-informative to help in performing a regression task. Incorporating a prior knowledge to this type of problem might offer a promising solution. In this study, the proposed algorithm translated a given prior knowledge and the available samples into a function space before introducing the idea of Pareto optimality concept to the problem. Instead of a single optimal solution competing with the objectives, the algorithm provides a set of solutions, generally denoted as the Pareto-optimal that offers more flexibility towards the intended solution. Thus the corresponding trade-off between solutions can be chosen in the presence of preference information. The proposed technique also does not require the addition of equality or non-equality constraints in introducing a prior knowledge. We also discussed, the challenges of determining the two objective functions that to be defined in the multi-objective problem environment. A benchmark function is used to validate the proposed technique, and it is shown that prior knowledge incorporation can relatively improve the regression performance.