Bias-Corrected Hierarchical Bayesian Classification With a Selected Subset of High-Dimensional Features
Bibliographic record
Abstract
Abstract Class prediction based on high-dimensional features has received a great deal of attention in many areas of application. For example, biologists are interested in using microarray gene expression profiles for diagnosis or prognosis of a certain disease (e.g., cancer). For computational and other reasons, it is necessary to select a subset of features before fitting a statistical model, by evaluating how strongly the features are related to the response. However, such a feature selection procedure will result in overconfident predictive probabilities for future cases, because the signal-to-noise ratio in the retained features is exacerbated by the feature selection. In this article we develop a hierarchical Bayesian classification method that can correct for this feature selection bias. Our method, which we term bias-corrected Bayesian classification with selected features (BCBCSF), uses the partial information from the feature selection procedure, in addition to the retained features, to form a correct (unbiased) posterior distribution of certain hyperparameters in the hierarchical Bayesian model that control the signal-to-noise ratio of the dataset. We take a Markov chain Monte Carlo (MCMC) approach to inferring the model parameters. We then use MCMC samples to make predictions for future cases. Because of the simplicity of the models, the inferred parameters from MCMC are easy to interpret, and the computation is very fast. Simulation studies and tests with two real microarray datasets related to complex human diseases show that our BCBCSF method provides better predictions than two widely used high-dimensional classification methods, prediction analysis for microarrays and diagonal linear discriminant analysis. The R package BCBCSF for the method described here is available from http://math.usask.ca/longhai/software/BCBCSF and CRAN. KEY WORDS: Feature selectionHigh-dimensional classificationOptimistic bias Acknowledgments This work was supported by fundings from Natural Sciences and Engineering Research Council of Canada, and Canadian Foundation for Innovation. The author also thanks JASA editors and two anonymous referees for their great help in improving the previous drafts.
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How this classification was reachedexpand
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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".