# Collaborative Imputation of Urban Time Series through Cross-city Meta-learning

arXiv: https://arxiv.org/abs/2501.11306 · HTML: https://mlsanity.com/paper/2501.11306/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 51 of its 83 references that are in the map.
- First posted on arXiv 20 Jan 2025.

## Builds on (most cited first, 30 of 51)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [Large Models for Time Series and Spatio-Temporal Data: A Survey and Outlook](https://mlsanity.com/paper/2310.10196/) (2023)
- [The Capacity and Robustness Trade-off: Revisiting the Channel Independent Strategy for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2304.05206/) (2023)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [Interpolation-Prediction Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/1909.07782/) (2019)
- [UrbanGPT: Spatio-Temporal Large Language Models](https://mlsanity.com/paper/2403.00813/) (2024)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [Learning from Multiple Cities: A Meta-Learning Approach for Spatial-Temporal Prediction](https://mlsanity.com/paper/1901.08518/) (2019)
- [A Survey on Time-Series Pre-Trained Models](https://mlsanity.com/paper/2305.10716/) (2023)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Learning Signal-Agnostic Manifolds of Neural Fields](https://mlsanity.com/paper/2111.06387/) (2021)
- [Spatio-Temporal Graph Few-Shot Learning with Cross-City Knowledge Transfer](https://mlsanity.com/paper/2205.13947/) (2022)
- [Learning from Irregularly-Sampled Time Series: A Missing Data Perspective](https://mlsanity.com/paper/2008.07599/) (2020)

## Abstract (arXiv)

Urban time series, such as mobility flows, energy consumption, and pollution records, encapsulate complex urban dynamics and structures. However, data collection in each city is impeded by technical challenges such as budget limitations and sensor failures, necessitating effective data imputation techniques that can enhance data quality and reliability. Existing imputation models, categorized into learning-based and analytics-based paradigms, grapple with the trade-off between capacity and generalizability. Collaborative learning to reconstruct data across multiple cities holds the promise of breaking this trade-off. Nevertheless, urban data's inherent irregularity and heterogeneity issues exacerbate challenges of knowledge sharing and collaboration across cities. To address these limitations, we propose a novel collaborative imputation paradigm leveraging meta-learned implicit neural representations (INRs). INRs offer a continuous mapping from domain coordinates to target values, integrating the strengths of both paradigms. By imposing embedding theory, we first employ continuous parameterization to handle irregularity and reconstruct the dynamical system. We then introduce a cross-city collaborative learning scheme through model-agnostic meta learning, incorporating hierarchical modulation and normalization techniques to accommodate multiscale representations and reduce variance in response to heterogeneity. Extensive experiments on a diverse urban dataset from 20 global cities demonstrate our model's superior imputation performance and generalizability, underscoring the effectiveness of collaborative imputation in resource-constrained settings.