
Best Subset Selection in Reduced Rank Regression
Reduced rank regression is popularly used for modeling the relationship ...
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Selection consistency of Lassobased procedures for misspecified highdimensional binary model and random regressors
We consider selection of random predictors for highdimensional regressi...
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On the use of information criteria for subset selection in least squares regression
Least squares (LS) based subset selection methods are popular in linear ...
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Nested Kriging predictions for datasets with large number of observations
This work falls within the context of predicting the value of a real fun...
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Efficient Subpixel Refinement with Symbolic Linear Predictors
We present an efficient subpixel refinement method usinga learningbased...
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Approximate is Good Enough: Probabilistic Variants of Dimensional and Margin Complexity
We present and study approximate notions of dimensional and margin compl...
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Bayesian crack detection in ultra high resolution multimodal images of paintings
The preservation of our cultural heritage is of paramount importance. Th...
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Conditional Uncorrelation and Efficient Nonapproximate Subset Selection in Sparse Regression
Given m ddimensional responsors and n ddimensional predictors, sparse regression finds at most k predictors for each responsor for linearly approximation, 1≤ k ≤ d1. The key problem in sparse regression is subset selection, which usually suffers from the high computational cost. Here we consider sparse regression from the view of correlation, and propose the formula of conditional uncorrelation. Then an efficient nonapproximate method of subset selection is proposed in which we do not need to calculate any linear coefficients for the candidate predictors. By the proposed method, the computational complexity is reduced from O(1/2k^3+kd) to O(1/3k^3) for each candidate subset in sparse regression. Because the dimension d is generally the number of observations or experiments and large enough, the proposed method can significantly improve the efficiency of sparse regression.
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