Kernel Partial Least Squares is Universally Consistent

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Kernel Partial Least Squares is Universally Consistent
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as the solution of a global cost minimization procedure over a fixed model nor is it a linear estimator. Instead, approximate solutions are constructed by projections onto a nested set of data-dependent subspaces. To prove consistency, we exploit the known fact that Partial Least Squares is equivalent to the conjugate gradient algorithm in combination with early stopping. The choice of the stopping rule (number of iterations) is a crucial point. We study two empirical stopping rules. The first one monitors the estimation error in each iteration step of Partial Least Squares, and the second one estimates the empirical complexity in terms of a condition number. Both stopping...
Gilles Blanchard, Nicole Krämer
Added 19 May 2011
Updated 19 May 2011
Type Journal
Year 2010
Where JMLR
Authors Gilles Blanchard, Nicole Krämer
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