1 research outputs found
Learning the kernel matrix via predictive low-rank approximations
Efficient and accurate low-rank approximations of multiple data sources are
essential in the era of big data. The scaling of kernel-based learning
algorithms to large datasets is limited by the O(n^2) computation and storage
complexity of the full kernel matrix, which is required by most of the recent
kernel learning algorithms.
We present the Mklaren algorithm to approximate multiple kernel matrices
learn a regression model, which is entirely based on geometrical concepts. The
algorithm does not require access to full kernel matrices yet it accounts for
the correlations between all kernels. It uses Incomplete Cholesky
decomposition, where pivot selection is based on least-angle regression in the
combined, low-dimensional feature space. The algorithm has linear complexity in
the number of data points and kernels. When explicit feature space induced by
the kernel can be constructed, a mapping from the dual to the primal Ridge
regression weights is used for model interpretation.
The Mklaren algorithm was tested on eight standard regression datasets. It
outperforms contemporary kernel matrix approximation approaches when learning
with multiple kernels. It identifies relevant kernels, achieving highest
explained variance than other multiple kernel learning methods for the same
number of iterations. Test accuracy, equivalent to the one using full kernel
matrices, was achieved with at significantly lower approximation ranks. A
difference in run times of two orders of magnitude was observed when either the
number of samples or kernels exceeds 3000.Comment: 10 pages, 4 figure