Block coordinate descent algorithm improves variable selection and estimation in error‐in‐variables regression
Why this work is in the frame
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Bibliographic record
Abstract
Medical research increasingly includes high-dimensional regression modeling with a need for error-in-variables methods. The Convex Conditioned Lasso (CoCoLasso) utilizes a reformulated Lasso objective function and an error-corrected cross-validation to enable error-in-variables regression, but requires heavy computations. Here, we develop a Block coordinate Descent Convex Conditioned Lasso (BDCoCoLasso) algorithm for modeling high-dimensional data that are only partially corrupted by measurement error. This algorithm separately optimizes the estimation of the uncorrupted and corrupted features in an iterative manner to reduce computational cost, with a specially calibrated formulation of cross-validation error. Through simulations, we show that the BDCoCoLasso algorithm successfully copes with much larger feature sets than CoCoLasso, and as expected, outperforms the naïve Lasso with enhanced estimation accuracy and consistency, as the intensity and complexity of measurement errors increase. Also, a new smoothly clipped absolute deviation penalization option is added that may be appropriate for some data sets. We apply the BDCoCoLasso algorithm to data selected from the UK Biobank. We develop and showcase the utility of covariate-adjusted genetic risk scores for body mass index, bone mineral density, and lifespan. We demonstrate that by leveraging more information than the naïve Lasso in partially corrupted data, the BDCoCoLasso may achieve higher prediction accuracy. These innovations, together with an R package, BDCoCoLasso, make error-in-variables adjustments more accessible for high-dimensional data sets. We posit the BDCoCoLasso algorithm has the potential to be widely applied in various fields, including genomics-facilitated personalized medicine research.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it