# GOPHER: Categorical probabilistic forecasting with graph structure via local continuous-time dynamics

arXiv: https://arxiv.org/abs/2112.09964 · HTML: https://mlsanity.com/paper/2112.09964/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 18 Dec 2021.

## Builds on (most cited first, 18 of 18)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Riemannian Continuous Normalizing Flows](https://mlsanity.com/paper/2006.10605/) (2020)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Neural Manifold Ordinary Differential Equations](https://mlsanity.com/paper/2006.10254/) (2020)
- [Learning continuous-time PDEs from sparse data with graph neural networks](https://mlsanity.com/paper/2006.08956/) (2020)
- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems](https://mlsanity.com/paper/2011.10616/) (2020)
- [Continuous-Depth Neural Models for Dynamic Graph Prediction](https://mlsanity.com/paper/2106.11581/) (2021)

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

- [Veagle: Advancements in Multimodal Representation Learning](https://mlsanity.com/paper/2403.08773/) (2024)

## Abstract (arXiv)

We consider the problem of probabilistic forecasting over categories with graph structure, where the dynamics at a vertex depends on its local connectivity structure. We present GOPHER, a method that combines the inductive bias of graph neural networks with neural ODEs to capture the intrinsic local continuous-time dynamics of our probabilistic forecasts. We study the benefits of these two inductive biases by comparing against baseline models that help disentangle the benefits of each. We find that capturing the graph structure is crucial for accurate in-domain probabilistic predictions and more sample efficient models. Surprisingly, our experiments demonstrate that the continuous time evolution inductive bias brings little to no benefit despite reflecting the true probability dynamics.