Mixture robust L1 probabilistic principal component regression and soft sensor application
Bibliographic record
Abstract
Abstract In this paper, the multivariate Laplace distribution (also called L1 distribution) is adopted to construct a robust probabilistic principal component regression model (MRPPCR‐L1) under multiple operating modes. In the practical industrial chemistry process, outliers exist due to incorrect recording, disturbances, and process noises and might result in modelling distortion. To address this problem, Laplace distribution, instead of the Gaussian distribution in traditional methods, is introduced to reduce the negative influence of outliers. Moreover, probabilistic principal component regression is employed for dealing with the mixture modelling problem owing to its probabilistic property to determine the operating modes. The formulation of this approach is derived with the expectation maximum algorithm and the soft sensing model is also developed for prediction. Compared to the conventional method, a numerical example and the Tennessee Eastman process are used to demonstrate the robust modelling performance of the proposed method.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 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".