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Guarding against Spurious Discoveries in High Dimensions.
1Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544.
Journal of Machine Learning Research : JMLR
|September 23, 2017
Summary
This study introduces a goodness of spurious fit measure to statistically validate data-mining discoveries. The LAMM algorithm helps distinguish real findings from chance correlations in high-dimensional data analysis.
Area of Science:
- Statistics
- Machine Learning
- Data Mining
Background:
- High-dimensional data analysis presents challenges with spurious discoveries due to numerous variable selection possibilities.
- Statistical validation is crucial to differentiate genuine findings from chance associations.
Purpose of the Study:
- To define and compute a measure of goodness of spurious fit to assess the validity of covariate-response variable associations.
- To develop a robust algorithm for computing this measure and establish its asymptotic distribution.
Main Methods:
- Definition of a goodness of spurious fit measure, generalizing maximum spurious correlation.
- Development and application of the LAMM algorithm for computation.
- Derivation of the asymptotic distribution for generalized linear models and L1-regression, estimated via multiplier bootstrapping.
Main Results:
- The goodness of spurious fit measure quantifies how well a response variable can be fitted by an optimal subset of covariates under a null model.
- The derived asymptotic distribution depends on sample size, dimension, selected variables, and covariance information.
- Multiplier bootstrapping provides consistent estimation for the asymptotic distribution.
Conclusions:
- The proposed method and LAMM algorithm offer a benchmark to guard against spurious discoveries in high-dimensional data.
- The goodness of spurious fit measure can be applied to model selection, prioritizing models with superior performance over chance fits.
- The approach is validated through simulations and an application to neuroblastoma trial data.
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