M<sup>2</sup>D-VAE: Self-Supervised Probabilistic Temporal–Spatial Latent Representation Learning for Unsupervised Industrial Operational Applications Under Missing Value Interference
Bibliographic record
Abstract
Due to sensor malfunctions and data transmission corruptions, the industrial process data collected commonly contain missing values. It poses a significant challenge for data-driven approaches in aggregating temporal-spatial correlations that reflect dependencies across both variables and times, which makes it difficult to directly carry out downstream industrial operational applications. In this study, a self-supervised representation learning model is proposed to extract probabilistic temporal-spatial latent variables (LVs) from sequential data under missing value interference. The extracted LVs can be utilized for typical industrial operational applications through a unified framework. First, a novel deep dynamic probabilistic latent variable model, named Markov dynamic variational autoencoder (MD-VAE), is proposed to explicitly model the temporal-spatial dependencies between LVs. The latent posteriors are Bayesian smoothed by global sequence information for effective variational inference (VI). Second, a self-supervised learning approach, termed masked MD-VAE (M2D-VAE), is proposed to address the challenge of directly extracting temporal-spatial LVs under missing value interference. Controllable constraints with practical interpretations are introduced to balance the latent bottleneck capacity with reconstruction accuracy during model optimization. A unified framework is proposed to utilize the latent representations for typical industrial downstream tasks. Case studies conducted on a real-world multiphase flow process demonstrate the superiority of M2D-VAE in unsupervised industrial operational applications including missing value imputation and dynamic process monitoring under missing value interference.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".