High-dimensional graphical models for noisy data
Bibliographic record
Abstract
The problem of estimating the inverse covariance or precision matrix for graphical models under a high-dimensional setting is a well-known challenge in modern statistics.Numerous theoretical and applied works have been proposed to date, particularly when the data are fully observed and follow a multivariate normal distribution.However, in the presence of measurement errors, such as additive or multiplicative errors, different surrogate estimates have been suggested in the literature to obtain unbiased estimates of the true covariance matrix.Unfortunately, these surrogate estimators may not necessarily be positive semi-definite, leading to a non-convex objective function.To address this issue, the surrogate estimators can be projected onto the nearest positive semi-definite matrix, transforming the objective function into a convex problem.While consistency bounds for tail deviations of the estimated and true covariance matrix have been well-studied for fully observed data with sub-Gaussian distributions or bounded moments, such bounds have not been established for the presence of measurement errors.Therefore, the first part of this thesis focuses on developing consistency bounds for random variables that are sub-Gaussian or have bounded moments in the presence of additive or multiplicative measurement errors.We also perform simulation studies and real data analysis to compare the performance of the covariance projection method with existing methods for precision matrix estimation for corrupted data.i Next, we address the problem of joint estimation of regression coefficients and precision matrix in the presence of missing data, a common issue in genetics.We restrict our attention to the scenario where both the data and measurement error are sub-Gaussian.We employ similar techniques to project the surrogate estimate of the sample covariance matrix to ensure convexity of the objective function and derive consistency bounds.Additionally, we conduct simulation studies to compare our method with existing approaches.
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.007 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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".