Valid post-selection and post-regularization inference: An elementary, general approach
Bibliographic record
Abstract
Here we present an expository, general analysis of valid post-selection or post-regularization inference about a low-dimensional target parameter in the presence of a very high-dimensional nuisance parameter which is estimated using selection or regularization methods. Our analysis provides a set of high-level conditions under which inference for the low-dimensional parameter based on testing or point estimation methods will be regular despite selection or regularization biases occurring in estimation of the high-dimensional nuisance parameter. The results may be applied to establish uniform validity of post-selection or post-regularization inference procedures for low-dimensional target parameters over large classes of models. The high-level conditions allow one to clearly see the types of structure needed for achieving valid post-regularization inference and encompass many existing results. A key element of the structure we employ and discuss in detail is the use of orthogonal or "immunized" estimating equations that are locally insensitive to small mistakes in estimation of the high-dimensional nuisance parameter. As an illustration, we use the high-level conditions to provide readily verifiable sufficient conditions for a class of affine-quadratic models that include the usual linear model and linear instrumental variables model as special cases. As a further application and illustration, we use these results to provide an analysis of post-selection inference in a linear instrumental variables model with many regressors and many instruments. We conclude with a review of other developments in post-selection inference and note that many of the developments can be viewed as special cases of the general encompassing framework of orthogonal estimating equations provided in this paper.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.037 | 0.089 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.009 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.004 | 0.008 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".