Independent Component Analysis for Uncertainty Representation of Stochastic Systems
Bibliographic record
Abstract
The predictive accuracy of stochastic systems depends on the calibration accuracy of its uncertain parameters modelled as random process. The probabilistic representation of these uncertain parameters can be achieved by Karhunen-Loeve Expansion (KLE) in which a random process is approximated by a set of decorrelated (statistically orthogonal) random variables. For a non-Gaussian process, although the set of random variables resulting from KLE expansion are pair-wise decorrelated, they are not generally independent. The lack of independence among these random quantities demands computationally intensive joint statistical characterisations (e.g. estimation of a joint probability distribution function). This paper explores the possibility of an alternative representation of a non-Gaussian stochastic process by a set of independent (or as independent as possible) random variables using Independent Component Analysis (ICA). The approach approximates a non-Gaussian random process by a set of random variables satisfying higher order decorrelation properties. The mathematical framework is elucidated from the context of its application to stochastic partial differential equations in mechanics.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| 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 |
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".