Link Representation Learning for Probabilistic Travel Time Estimation
Bibliographic record
Abstract
Travel time estimation is a key task in navigation apps and web mapping services. Existing deterministic and probabilistic methods, based on the assumption of trip independence, predominantly focus on modeling individual trips while overlooking trip correlations. However, real-world conditions frequently introduce strong correlations between trips, influenced by external and internal factors such as weather and the tendencies of drivers. To address this, we propose a deep hierarchical joint probabilistic model, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ProbETA</i>, for travel time estimation, capturing both inter-trip and intra-trip correlations. The joint distribution of travel times across multiple trips is modeled as a low-rank multivariate Gaussian, parameterized by learnable link representations estimated using the empirical Bayes approach. We also introduce a data augmentation method based on trip sub-sampling, allowing for fine-grained gradient backpropagation when learning link representations. During inference, our model estimates the probability distribution of travel time for a queried trip, conditional on spatiotemporally adjacent completed trips. Evaluation on two real-world GPS trajectory datasets demonstrates that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ProbETA</i> outperforms state-of-the-art deterministic and probabilistic baselines, with Mean Absolute Percentage Error decreasing by over 12.60%. Moreover, the learned link representations align with the physical network geometry, potentially making them applicable for other tasks.
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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".