Neural Computation
Some large-scale matrix computation problems
Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
Approximation of the Determinant of Large Sparse Symmetric Positive Definite Matrices
SIAM Journal on Matrix Analysis and Applications
Model selection with the Loss Rank Principle
Computational Statistics & Data Analysis
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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 (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 only depends 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.