Multiobjective model selection for non-linear regression techniques

This paper proposes to model the critical issue of the choice of the free parameters of a supervised non-linear regression technique (the so called model selection issue) as a multiobjective optimization problem. In this framework, the multi-objective function is made up of a set of two or more quality metrics (e.g., MSE, R², etc.) computed on the test (or validation) samples. A set of solutions is derived according to the concept of Pareto optimality. The advantages of the proposed approach with respect to the traditional ones (which typically optimize a single scalar metric) are mainly two: (1) the capability to derive solutions which jointly optimize the set of metrics considered and represent different possible optimal tradeoffs among them; and (2) the possibility for the user to effectively select the model that optimizes the requirements of the specific retrieval problem. Results achieved for the specific application of soil moisture estimation from microwave remotely sensed data with the Support Vector Regression (SVR) technique are reported. These results show the effectiveness of the proposed approach.