A computer-implemented method for simultaneous metric learning and variable selection in non-linear regression is presented. The computer-implemented method includes introducing a dataset and a target variable, creating a univariate neighborhood probability map for each reference point of the dataset, and determining a pairwise distance between each reference point and other points within the dataset. The computer-implemented method further includes computing a Hessian matrix of a quadratic programming (QP) problem, performing optimization of the QP problem, re-weighing data derived from the optimization of the QP problem, and performing non-linear regression on the re-weighed data.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A computer-implemented method executed on a processor for simultaneous metric learning and variable selection in non-linear regression, the method comprising: introducing a dataset and a target variable; creating a univariate neighborhood probability map for each reference point of the dataset; determining a pairwise distance between each reference point and other points within the dataset; based on determined pairwise distances, computing a Hessian matrix of a quadratic programming (QP) problem; performing optimization of the QP problem; re-weighing data derived from the optimization of the QP problem; and performing non-linear regression on the re-weighed data. 2. The method of claim 1, wherein the target variable is a continuous target variable and the dataset includes a plurality of input variables that are correlated to the continuous target variable. 3. The method of claim 1, wherein the optimization of the QP problem is a concave-convex optimization. 4. The method of claim 3, wherein the concave-convex optimization of the QP problem is performed by a majorization-minimization algorithm. 5. The method of claim 1, wherein the non-linear regression involves Gaussian process regression or support vector regression. 6. The method of claim 1, wherein re-weighing the data allows for learning an optimal non-negative scaling for each variable in the dataset. 7. The method of claim 1, wherein a neighborhood structure is optimized simultaneously with a metric parameter. 8. A system for simultaneous metric learning and variable selection in non-linear regression, the system comprising: a memory; and a processor in communication with the memory, wherein the processor is configured to: introduce a dataset and a target variable; create a univariate neighborhood probability map for each reference point of the dataset; determine a pairwise distance between each reference point and other points within the dataset; based on determined pairwise distances, compute a Hessian matrix of a quadratic programming (QP) problem; perform optimization of the QP problem; re-weigh data derived from the optimization of the QP problem; and perform non-linear regression on the re-weighed data. 9. The system of claim 8, wherein the target variable is a continuous target variable and the dataset includes a plurality of input variables that are correlated to the continuous target variable. 10. The system of claim 8, wherein the optimization of the QP problem is a concave-convex optimization. 11. The system of claim 10, wherein the concave-convex optimization of the QP problem is performed by a majorization-minimization algorithm. 12. The system of claim 8, wherein the non-linear regression involves Gaussian process regression or support vector regression. 13. The system of claim 8, wherein re-weighing the data allows for learning an optimal non-negative scaling for each variable in the dataset. 14. The system of claim 8, wherein a neighborhood structure is optimized simultaneously with a metric parameter. 15. A non-transitory computer-readable storage medium comprising a computer-readable program for simultaneous metric learning and variable selection in non-linear regression, wherein the computer-readable program when executed on a computer causes the computer to perform the steps of: introducing a dataset and a target variable; creating a univariate neighborhood probability map for each reference point of the dataset; determining a pairwise distance between each reference point and other points within the dataset; based on determined pairwise distances, computing a Hessian matrix of a quadratic programming (QP) problem; performing optimization of the QP problem; re-weighing data derived from the optimization of the QP problem; and performing non-linear regression on the re-weighed data. 16. The non-transitory computer-readable storage medium of claim 15, wherein the optimization of the QP problem is a concave-convex optimization. 17. The non-transitory computer-readable storage medium of claim 16, wherein the concave-convex optimization of the QP problem is performed by a majorization-minimization algorithm. 18. The non-transitory computer-readable storage medium of claim 15, wherein the non-linear regression involves Gaussian process regression or support vector regression. 19. The non-transitory computer-readable storage medium of claim 15, wherein re-weighing the data allows for learning an optimal non-negative scaling for each variable in the dataset. 20. The non-transitory computer-readable storage medium of claim 15, wherein a neighborhood structure is optimized simultaneously with a metric parameter.