Mathematical improvements to maximum likelihood parallel factor analysis: theory and simulations
Bibliographic record
Abstract
Abstract A number of simplified algorithms for carrying out m aximum l ikelihood para llel fac tor analysis (MLPARAFAC) for three‐way data affected by different error structures are described. The MLPARAFAC method was introduced to establish the theoretical basis to treat heteroscedastic and/or correlated noise affecting trilinear data. Unfortunately, the large size of the error covariance matrix employed in the general formulation of this algorithm prevents its application to solve standard three‐way problems. The algorithms developed here are based on the principle of alternating least squares, but differ from the generalized MLPARAFAC algorithm in that they do not use equivalent alternatives of the objective function to estimate the loadings for the different modes. Instead, these simplified algorithms tackle the loss of symmetry of the PARAFAC model by using only one representation of the objective function to estimate the loadings of all of the modes. In addition, a compression step is introduced to allow the use of the generalized algorithm. Simulation studies carried out under a variety of measurement error conditions were used for statistical validation of the maximum likelihood properties of the algorithms and to assess the quality of the results and computation time. The simplified MLPARAFAC methods are also shown to produce more accurate results than PARAFAC under a variety of conditions. Copyright © 2005 John Wiley & Sons, Ltd.
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 machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".