Automatic Hierarchical Time-Series Forecasting Using Gaussian Processes
Bibliographic record
Abstract
Forecasting often involves multiple time-series that are hierarchically organized (e.g., sales by geography). In that case, there is a constraint that the bottom level forecasts add-up to the aggregated ones. Common approaches use traditional forecasting methods to predict all levels in the hierarchy and then reconcile the forecasts to satisfy that constraint. We propose a new algorithm that automatically forecasts multiple hierarchically organized time-series. We introduce a combination of additive Gaussian processes (GPs) with a hierarchical piece-wise linear function to estimate, respectively, the stationary and non-stationary components of the time-series. We define a flexible structure of additive GPs generated by each aggregated group in the hierarchy of the data. This formulation aims to capture the nested information in the hierarchy while avoiding overfitting. We extended the piece-wise linear function to be hierarchical by defining hyperparameters shared across related time-series. From our experiments, our algorithm can estimate hundreds of time-series at once. To work at this scale, the estimation of the posterior distributions of the parameters is performed using mean-field approximation. We validate the proposed method in two different real-world datasets showing its competitiveness when compared to the state-of-the-art approaches. In summary, our method simplifies the process of hierarchical forecasting as no reconciliation is required. It is easily adapted to non-Gaussian likelihoods and multiple or non-integer seasonalities. The fact that it is a Bayesian approach makes modeling uncertainty of the forecasts trivial.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.003 | 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".