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

The Loss Rank Criterion for Variable Selection in Linear Regression Analysis

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model selection criterion is proposed to select the best one among this preselected set. The approach leads to a fast and efficient procedure for variable selection, especially in high-dimensional settings. Model selection consistency of the suggested criterion is proven when the number of covariates d is fixed. Simulation studies suggest that the criterion still enjoys model selection consistency when d is much larger than the sample size. The simulations also show that our approach for variable selection works surprisingly well in comparison with existing competitors. The method is also applied to a real data set.Comment: 18 pages, 1 figur

Model Selection by Loss Rank for Classification and Unsupervised Learning

Hutter (2007) recently introduced the loss rank principle (LoRP) as a general purpose principle for model selection. The LoRP enjoys many attractive properties and deserves further investigations. The LoRP has been well-studied for regression framework in Hutter and Tran (2010). In this paper, we study the LoRP for classification framework, and develop it further for model selection problems in unsupervised learning where the main interest is to describe the associations between input measurements, like cluster analysis or graphical modelling. Theoretical properties and simulation studies are presented

Some perspectives on the problem of model selection

Ph.DDOCTOR OF PHILOSOPH

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 (k NN) 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 k NN

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 () 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 .