Model Comparison and Sparse Learning of Nonlinear Physics-Based Models Using Bayesian Inference
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
This thesis addresses the issue of overfitting while calibrating over-parameterized physical models with noisy and incomplete observations. A Bayesian inversion framework is augmented with model comparison and sparse learning algorithms to identify the optimal model nested under an over-parameterized model. The work is performed in three stages. First, the evidencebased Bayesian model comparison is implemented to rank competing models whereby the evidence is estimated using stationary samples from the posterior parameter probability density function (pdf) generated using a parallel and adaptive Markov Chain Monte Carlo (MCMC) sampler. Second, the concept of automatic relevance determination (ARD) is exploited to reformulate the model comparison problem into a sparse learning problem to alleviate the practical issues of 1) sensitivity of model evidence to prior pdf, and 2) overlooking nested models excluded in the candidate model set. ARD operates by assigning a zero-mean and unknown precision (hyperparameter) prior pdf to questionable model parameters. This ARD-based sparse learning approach is implemented using an MCMC-based evidence estimator and a gradientfree evidence optimizer to compute the optimal hyperparameters, which thereby picks out the optimal nested model. Third, a semi-analytical approach of nonlinear sparse Bayesian learning (NSBL) is proposed to alleviate the computational burden of the MCMC sampling within an optimization task. The analytical tractability of Bayesian entities is enabled by the Gaussian mixture-model approximation of the posterior parameter pdf without the ARD priors. A multistart Newton's method is designed to expedite the non-convex, unconstrained maximization of evidence using semi-analytically computed gradient and Hessian information of evidence.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 it