Adaptive First-Order Methods for General Sparse Inverse Covariance Selection
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Bibliographic record
Abstract
In this paper we consider estimating sparse inverse covariance of a Gaussian graphical model whose conditional independence is assumed to be partially known. Similarly as in [A. d'Aspremont, O. Banerjee, and L. El Ghaoui, SIAM J. Matrix Anal. Appl., 30 (2008), pp. 56–66; M. Yuan and Y. Lin, Biometrika, 94 (2007), pp. 19–35], we formulate it as an $l_1$-norm penalized maximum likelihood estimation problem. Further, we propose an algorithm framework, and develop two first-order methods, that is, the adaptive spectral projected gradient (ASPG) method and the adaptive Nesterov's smooth (ANS) method, for solving this estimation problem. Finally, we compare the performance of these two methods with glasso [J. Friedman, T. Hastie, and R. Tibshirani, Biostatistics, 9 (2008), pp. 432–441; J. Friedman, T. Hastie, and R. Tibshirani, Glasso: Graphical Lasso for R, Software package, Department of Statistics, Stanford University, Stanford, CA, 2007] on a set of randomly generated instances. Our computational results demonstrate that our methods are capable of solving problems of size at least a thousand and number of constraints of nearly a half million within a reasonable amount of time, and moreover, that the ASPG method generally outperforms the ANS method and glasso.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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