Simultaneous estimation of sub-model number and parameters for mixture probability principal component regression
Bibliographic record
Abstract
Principal component analysis (PCA) is a proven technology in data analytics for modeling, monitoring and optimization of high-dimensional and large-scale processes. However, traditional PCA lacks of probabilistic interpretation, limiting its ability of inference. Probabilistic Principal Component Regression (PPCR) is a probabilistic counterpart of Principal Component Regression (PCR) that has good probability interpretation. In order to deal with nonlinearities as well as multi-mode behavior, it has been extended to mixture PPCR (MPPCR). To build a model for a multi-mode system, the associated problem with MPPCR is to estimate the number of mixture components which has been an open problem. In this paper, we propose a hierarchical MPPCR approach for automatically estimating the number of components. This method is based on a divisive hierarchical algorithm, and initially starts with the minimum possible number of components. At each stage, the decision for splitting the components is made based on the Minimum Message Length (MML) criterion. In addition, a merging step is proposed for detected highly overlapped components that controls the splitting step performance. Furthermore, the developed hierarchical MPPCR model is solved through maximum a posteriori (MAP) principle under the expectation-maximization (EM) algorithm in order to utilize prior distributions. Finally, a simulation example is presented to demonstrate the model performance.
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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".