# Learning Higher-Order Interactions from Incomplete Spatiotemporal Data with Mixtures of Hypergraph Laplacians

arXiv: https://arxiv.org/abs/2605.17316 · HTML: https://mlsanity.com/paper/2605.17316/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 17 May 2026.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [The physics of higher-order interactions in complex systems](https://mlsanity.com/paper/2110.06023/) (2021)
- [Bayesian Temporal Factorization for Multidimensional Time Series Prediction](https://mlsanity.com/paper/1910.06366/) (2019)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [How Much and When Do We Need Higher-order Information in Hypergraphs? A Case Study on Hyperedge Prediction](https://mlsanity.com/paper/2001.11181/) (2020)
- [Tensor Completion for Weakly-dependent Data on Graph for Metro Passenger Flow Prediction](https://mlsanity.com/paper/1912.05693/) (2019)
- [A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2003.10271/) (2020)
- [Laplacian Convolutional Representation for Traffic Time Series Imputation](https://mlsanity.com/paper/2212.01529/) (2022)
- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [Representing higher-order dependencies in networks](https://mlsanity.com/paper/1508.03113/) (2015)
- [Hypergraph-based Motion Generation with Multi-modal Interaction Relational Reasoning](https://mlsanity.com/paper/2409.11676/) (2024)
- [AI2-Active Safety: AI-enabled Interaction-aware Active Safety Analysis with Vehicle Dynamics](https://mlsanity.com/paper/2505.00322/) (2025)
- [The temporal dynamics of group interactions in higher-order social networks](https://mlsanity.com/paper/2306.09967/) (2023)
- [Residual Enhanced Multi-Hypergraph Neural Network](https://mlsanity.com/paper/2105.00490/) (2021)
- [Knowledge Is Not Static: Order-Aware Hypergraph RAG for Language Models](https://mlsanity.com/paper/2604.12185/) (2026)

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

- [Forecasting the Emergence and Evolution of Crash Hotspots: A Unified Deep Learning Framework for Proactive Traffic Safety](https://mlsanity.com/paper/2607.24168/) (2026)

## Abstract (arXiv)

Traffic sensor data exhibit strong temporal and cross-sensor dependencies, yet long gaps erase both a sensor's local history and the joint observations needed to learn its relationships with other sensors. We introduce MoHL, a mixture of hypergraph Laplacians that learns group-wise relational structure directly from incomplete spatiotemporal data. MoHL discovers overlapping sensor groups from observed co-variation, constructs a Laplacian component for each interaction order, and learns their mixture through holdouts that mimic the missingness pattern. By sharing weights across group-induced couplings, MoHL pools scattered evidence instead of estimating each coupling independently. We characterize the induced weight-sharing structure and analyze the conditions under which sharing reduces estimation risk. Experiments on three traffic networks show that higher-order groups are most beneficial under long gaps, while support-matched comparisons demonstrate the advantage of shared weights when relational evidence is scarce. MoHL achieves the lowest error among the evaluated baseline methods under day-long gaps, with orders of magnitude fewer learned parameters than deep imputers. These results show how group-wise sharing can sustain reliable reconstruction precisely when missingness depletes the evidence needed to learn cross-sensor dependence.