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Controlling the local false discovery rate in the adaptive Lasso
Joshua N Sampson1, Nilanjan Chatterjee, Raymond J Carroll
1Division of Cancer Epidemiology and Genetics, National Cancer Institute, 6120 Executive Blvd, EPS 8038, Rockville, MD 20852, USA.
Biostatistics (Oxford, England)
|April 12, 2013
Summary
This study introduces a new method using local false discovery rates (lFDRs) to improve variable selection in adaptive Lasso models. The approach helps reduce false positives, leading to more accurate statistical models.
Area of Science:
- Statistics
- Biostatistics
- Machine Learning
Background:
- The Lasso procedure is popular for variable selection by shrinking coefficients to zero.
- Adaptive Lasso enhances Lasso using data-adaptive weights but can produce false positives.
- Existing methods lack robust control over false discoveries in adaptive Lasso models.
Purpose of the Study:
- To adapt local false discovery rates (lFDRs) for the adaptive Lasso procedure.
- To provide a method for selecting smoothing parameters (λn) to control lFDRs.
- To compare lFDR-controlled selection with oracle property-based selection.
Main Methods:
- Defined lFDR for adaptive Lasso smoothing parameters (λn).
- Derived the relationship between lFDR and λn.
- Proposed a method to select λn for a desired lFDR.
- Utilized simulation studies and a prostate-specific antigen genetic dataset.
Main Results:
- Demonstrated that traditional smoothing parameters yield lFDR=1.
- Showed how to select λn to achieve a specified lFDR.
- Compared coefficient estimates from lFDR-selected and oracle-selected models.
- Identified reduced false positives in the lFDR-based approach.
Conclusions:
- The proposed lFDR adaptation offers a principled way to control false discoveries in adaptive Lasso.
- This method improves model interpretability and reliability by reducing spurious variable inclusions.
- The approach is validated through simulations and a real-world genetic study.
