Temporally Chained Equations: An Interpretable Missing Data Imputation Approach for Smart Meters with Low Data Requirements
Bibliographic record
Abstract
Smart grids enable real-time monitoring and optimization of energy generation, transmission, and consumption. Ensuring the integrity of data collected by smart meters is crucial for grid operation and data-driven decision-making, but missing data due to communication failures or device malfunctions can compromise data reliability. Recent studies have proposed deep learning techniques to impute missing points; however, these models require large training data, are computationally expensive, and struggle to scale to a large consumer base. Moreover, the interpretability of the imputation is also a concern, hindering trust and acceptance. To address these issues, this paper proposes Temporally Chained Equations (TCE), an interpretable, computationally lightweight missing data imputation approach for smart meters with low data requirements. TCE forms chained equations across the temporal axis using lead and lag features and imputes missing points in a manner coherent with neighboring and seasonally correlated points. Local normalization reduces the impact of outliers, and an iterative process refines the estimates until convergence. Experiments on a real-world dataset show that TCE outperforms related techniques, particularly for random missing points or short sequences of continuous missing points.
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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 | 0.008 | 0.025 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 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".