Browse By: |
Paper No. Title Author Adviser Topic Type Keyword |
Other Functions: |
Submit a Report Reload Repository View Credits |
| Paper No. | 2006-003 |
| Title | Local Minimax Function Approximation and Estimation with Optimal Finite Sample Error Bounds: Applications to Linear Regression, Boosting, Tree Learning, Kernel Machines and Inverse Problems |
| Author | Jones, Lee |
|
APA Format Citation |
Jones, L. (2006). Local Minimax Function Approximation and Estimation with Optimal Finite Sample Error Bounds: Applications to Linear Regression, Boosting, Tree Learning, Kernel Machines and Inverse Problems. Unpublished Research Paper No. 2006-003, University of Massachusetts Lowell, Dept. of Computer Science, Lowell, MA 01854. |
| Keywords | |
| On-Line Version |
http://teaching.cs.uml.edu/~heines/techrpts/Papers/JonesLocal.pdf Format = Adobe Acrobat PDF (if the above link is broken, please contact Prof. Jesse Heines) |
| Abstract |
A method of local minimax estimation is formulated for linear inverse problems and nonlinear regression which provides best mean squared error bounds for finite samples. Results are given for optimal local learning of approximately linear functions with side information (context) using classical geometry. Greedy additive expansions are then combined with local minimax learning via a change in metric. An optimal strategy is presented for constructing and fusing the estimators from the trees in a (random) forest. Local minimax learning is extended to kernel machines. Optimal imbeddings of truncated cones in balls of reproducing kernel Hilbert space are used to derive mean squared error bounds and estimators for probability of class membership in two class pattern classification problems. An algorithm is proposed which uses these bounds to determine best local kernel shape in vector machine learning. |