Bayesian Methods for Data Integration and High Dimensional Linear Model with Non-Sparsity
Bibliographic record
Abstract
We address data integration where correlated data are collected across multiple platforms, modeling responses and predictors linearly. We extend this framework by incorporating random errors from sub-Gaussian and sub-exponential distributions. The goal is to identify key predictors across platforms, even as the number of predictors and observations grows indefinitely. Our approach combines marginal response densities from multiple platforms into a composite likelihood and introduces a Bayesian model selection criterion. Under regularity conditions, this criterion consistently selects the true model, even with a diverging model size. When true models differ across platforms, our method recovers the union support of predictors—those relevant in at least one platform. We implement a Monte Carlo Markov Chain (MCMC) algorithm for model selection. Simulations show that integrating multiple platforms improves model selection accuracy. Applied to financial data, our method combines information from three indices, identifying key predictors and yielding a more accurate predictive model with lower mean squared error than single-source models. In high-dimensional regression, sparsity assumptions on regression coefficients often fail when most coefficients are nonzero, causing bias. To address this, we propose Bayesian Grouping-Gibbs Sampling (BGGS), which partitions coefficients into 𝑘 groups, enabling efficient high-dimensional sampling. We explore 𝑘-selection via simulations and recommend an "elbow plot" for optimal determination. Theoretical analysis ensures model selection consistency and bounded prediction error. Numerical experiments confirm BGGS’s advantage in estimation and prediction. Applied to financial data, it effectively identifies robust predictive models.
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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 | 0.018 | 0.054 |
| Meta-epidemiology (narrow) | 0.002 | 0.003 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.005 | 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".