Some Greedy Learning Algorithms for Sparse Regression and Classification with Mercer Kernels
Prasanth B. Nair, Arindam Choudhury, Andy J. Keane;
We present greedy learning algorithms for building sparse nonlinear regression
and classification models from observational data using Mercer kernels.
Our objective is to develop efficient numerical schemes for reducing the
training and runtime complexities of kernel-based algorithms applied to large
datasets. In the spirit of Natarajan's greedy algorithm (Natarajan, 1995),
we iteratively minimize the L2
$ loss function subject to a
specified constraint on the degree of sparsity required of the final model or
till a specified stopping criterion is reached.
We discuss various greedy criteria for basis
selection and numerical schemes for improving the robustness and
computational efficiency. Subsequently, algorithms based on residual
minimization and thin QR factorization are presented
for constructing sparse regression and classification models. During the
course of the incremental model construction, the algorithms are terminated
using model selection principles such as
the minimum descriptive length (MDL) and Akaike's information
criterion (AIC). Finally, experimental results on
benchmark data are presented to demonstrate the competitiveness
of the algorithms developed in this paper.