Linear Support Vector Regression with Linear Constraints
This work addresses the need for constrained regression in specific domains such as biomedical data and weather forecasting, but it is incremental as it extends existing SVR and SMO methods with linear constraints.
The paper tackles the problem of incorporating linear constraints into linear Support Vector Regression to embed prior knowledge like probability vectors or monotonicity, and demonstrates the estimator's performance on simulated and real datasets including biomedical and weather forecast applications.
This paper studies the addition of linear constraints to the Support Vector Regression (SVR) when the kernel is linear. Adding those constraints into the problem allows to add prior knowledge on the estimator obtained, such as finding probability vector or monotone data. We propose a generalization of the Sequential Minimal Optimization (SMO) algorithm for solving the optimization problem with linear constraints and prove its convergence. Then, practical performances of this estimator are shown on simulated and real datasets with different settings: non negative regression, regression onto the simplex for biomedical data and isotonic regression for weather forecast.