# Link Representation Learning for Probabilistic Travel Time Estimation

arXiv: https://arxiv.org/abs/2407.05895 · HTML: https://mlsanity.com/paper/2407.05895/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 8 Jul 2024.

## Builds on (most cited first, 11 of 11)

- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [ETA Prediction with Graph Neural Networks in Google Maps](https://mlsanity.com/paper/2108.11482/) (2021)
- [A Simple Baseline for Travel Time Estimation using Large-Scale Trip Data](https://mlsanity.com/paper/1512.08580/) (2015)
- [Trajectory Data Management and Mining: A Survey from Deep Learning to the LLM Era](https://mlsanity.com/paper/2403.14151/) (2024)
- [Origin-Destination Travel Time Oracle for Map-based Services](https://mlsanity.com/paper/2307.03048/) (2023)
- [Adjusting for Autocorrelated Errors in Neural Networks for Time Series](https://mlsanity.com/paper/2101.12578/) (2021)
- [A Unified Neural Network Approach for Estimating Travel Time and Distance for a Taxi Trip](https://mlsanity.com/paper/1710.04350/) (2017)
- [Fine-Grained Trajectory-based Travel Time Estimation for Multi-city Scenarios Based on Deep Meta-Learning](https://mlsanity.com/paper/2201.08017/) (2022)
- [Multitask Weakly Supervised Learning for Origin Destination Travel Time Estimation](https://mlsanity.com/paper/2301.05336/) (2023)
- [Representation learning of rare temporal conditions for travel time prediction](https://mlsanity.com/paper/2208.04667/) (2022)

## Built on by (most cited first, 1 of 1)

- [SPTTE: A Spatiotemporal Probabilistic Framework for Travel Time Estimation](https://mlsanity.com/paper/2411.18484/) (2024)

## Abstract (arXiv)

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 ProbETA 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 ProbETA 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.