5,882 research outputs found
Overlapping Optimized Schwarz Methods for Parabolic Equations in n-Dimensions
We introduce in this paper a new tool to prove the convergence of the
Overlapping Optimized Schwarz Methods with multisubdomains. The technique is
based on some estimates of the errors on the boundaries of the overlapping
strips. Our guiding example is an n-Dimensional Linear Parabolic Equation
Model Selection with the Loss Rank Principle
A key issue in statistics and machine learning is to automatically select the
"right" model complexity, e.g., the number of neighbors to be averaged over in
k nearest neighbor (kNN) regression or the polynomial degree in regression with
polynomials. We suggest a novel principle - the Loss Rank Principle (LoRP) -
for model selection in regression and classification. It is based on the loss
rank, which counts how many other (fictitious) data would be fitted better.
LoRP selects the model that has minimal loss rank. Unlike most penalized
maximum likelihood variants (AIC, BIC, MDL), LoRP depends only on the
regression functions and the loss function. It works without a stochastic noise
model, and is directly applicable to any non-parametric regressor, like kNN.Comment: 31 LaTeX pages, 1 figur
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