%0 Journal Article %1 lo_framework_2016 %A Lo, Adeline %A Chernoff, Herman %A Zheng, Tian %A Lo, Shaw-Hwa %D 2016 %J Proceedings of the National Academy of Sciences %K SNP, data, genomics, high-dimensional prediction, predictivity, selection variable %N 50 %P 14277--14282 %R 10.1073/pnas.1616647113 %T Framework for making better predictions by directly estimating variables’ predictivity %U http://www.pnas.org/content/113/50/14277 %V 113 %X We propose approaching prediction from a framework grounded in the theoretical correct prediction rate of a variable set as a parameter of interest. This framework allows us to define a measure of predictivity that enables assessing variable sets for, preferably high, predictivity. We first define the prediction rate for a variable set and consider, and ultimately reject, the naive estimator, a statistic based on the observed sample data, due to its inflated bias for moderate sample size and its sensitivity to noisy useless variables. We demonstrate that the II\textlessmml:math\textgreater\textlessmml:mi\textgreaterI\textless/mml:mi\textgreater\textless/mml:math\textgreater-score of the PR method of VS yields a relatively unbiased estimate of a parameter that is not sensitive to noisy variables and is a lower bound to the parameter of interest. Thus, the PR method using the II\textlessmml:math\textgreater\textlessmml:mi\textgreaterI\textless/mml:mi\textgreater\textless/mml:math\textgreater-score provides an effective approach to selecting highly predictive variables. We offer simulations and an application of the II\textlessmml:math\textgreater\textlessmml:mi\textgreaterI\textless/mml:mi\textgreater\textless/mml:math\textgreater-score on real data to demonstrate the statistic’s predictive performance on sample data. We conjecture that using the partition retention and II\textlessmml:math\textgreater\textlessmml:mi\textgreaterI\textless/mml:mi\textgreater\textless/mml:math\textgreater-score can aid in finding variable sets with promising prediction rates; however, further research in the avenue of sample-based measures of predictivity is much desired.

@article{lo_framework_2016, abstract = {We propose approaching prediction from a framework grounded in the theoretical correct prediction rate of a variable set as a parameter of interest. This framework allows us to define a measure of predictivity that enables assessing variable sets for, preferably high, predictivity. We first define the prediction rate for a variable set and consider, and ultimately reject, the naive estimator, a statistic based on the observed sample data, due to its inflated bias for moderate sample size and its sensitivity to noisy useless variables. We demonstrate that the II{\textless}mml:math{\textgreater}{\textless}mml:mi{\textgreater}I{\textless}/mml:mi{\textgreater}{\textless}/mml:math{\textgreater}-score of the PR method of VS yields a relatively unbiased estimate of a parameter that is not sensitive to noisy variables and is a lower bound to the parameter of interest. Thus, the PR method using the II{\textless}mml:math{\textgreater}{\textless}mml:mi{\textgreater}I{\textless}/mml:mi{\textgreater}{\textless}/mml:math{\textgreater}-score provides an effective approach to selecting highly predictive variables. We offer simulations and an application of the II{\textless}mml:math{\textgreater}{\textless}mml:mi{\textgreater}I{\textless}/mml:mi{\textgreater}{\textless}/mml:math{\textgreater}-score on real data to demonstrate the statistic’s predictive performance on sample data. We conjecture that using the partition retention and II{\textless}mml:math{\textgreater}{\textless}mml:mi{\textgreater}I{\textless}/mml:mi{\textgreater}{\textless}/mml:math{\textgreater}-score can aid in finding variable sets with promising prediction rates; however, further research in the avenue of sample-based measures of predictivity is much desired.}, added-at = {2017-01-09T13:57:26.000+0100}, author = {Lo, Adeline and Chernoff, Herman and Zheng, Tian and Lo, Shaw-Hwa}, biburl = {https://www.bibsonomy.org/bibtex/2f4452b1827950acd7c795812aa14afb2/yourwelcome}, doi = {10.1073/pnas.1616647113}, interhash = {5ee6a56b46e003157299a3e3d4552ac8}, intrahash = {f4452b1827950acd7c795812aa14afb2}, issn = {0027-8424, 1091-6490}, journal = {Proceedings of the National Academy of Sciences}, keywords = {SNP, data, genomics, high-dimensional prediction, predictivity, selection variable}, language = {en}, month = dec, number = 50, pages = {14277--14282}, pmid = {27911830}, timestamp = {2017-01-09T14:01:11.000+0100}, title = {Framework for making better predictions by directly estimating variables’ predictivity}, url = {http://www.pnas.org/content/113/50/14277}, urldate = {2017-01-02}, volume = 113, year = 2016 }