# Nonparametric Embeddings of Sparse High-Order Interaction Events

arXiv: https://arxiv.org/abs/2207.03639 · HTML: https://mlsanity.com/paper/2207.03639/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 59 references that are in the map.
- First posted on arXiv 8 Jul 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Warm Up Cold-start Advertisements: Improving CTR Predictions via Learning to Learn ID Embeddings](https://mlsanity.com/paper/1904.11547/) (2019)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)
- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Sparse graphs using exchangeable random measures](https://mlsanity.com/paper/1401.1137/) (2014)
- [Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Counts](https://mlsanity.com/paper/1506.03493/) (2015)
- [Distributed Flexible Nonlinear Tensor Factorization](https://mlsanity.com/paper/1604.07928/) (2016)
- [Poisson-Randomized Gamma Dynamical Systems](https://mlsanity.com/paper/1910.12991/) (2019)
- [DFacTo: Distributed Factorization of Tensors](https://mlsanity.com/paper/1406.4519/) (2014)
- [Bayesian Conditional Tensor Factorizations for High-Dimensional Classification](https://mlsanity.com/paper/1301.4950/) (2013)
- [Regularizing Matrix Factorization with User and Item Embeddings for Recommendation](https://mlsanity.com/paper/1809.00979/) (2018)
- [Zero-Truncated Poisson Tensor Factorization for Massive Binary Tensors](https://mlsanity.com/paper/1508.04210/) (2015)
- [Scalable Bayesian Non-Negative Tensor Factorization for Massive Count Data](https://mlsanity.com/paper/1508.04211/) (2015)

## Built on by (most cited first, 5 of 5)

- [Streaming Factor Trajectory Learning for Temporal Tensor Decomposition](https://mlsanity.com/paper/2310.17021/) (2023)
- [Dynamic Tensor Decomposition via Neural Diffusion-Reaction Processes](https://mlsanity.com/paper/2310.19666/) (2023)
- [Efficient Nonparametric Tensor Decomposition for Binary and Count Data](https://mlsanity.com/paper/2401.07711/) (2024)
- [Multi-Aspect Mining and Anomaly Detection for Heterogeneous Tensor Streams](https://mlsanity.com/paper/2602.04917/) (2026)
- [Arbitrarily Conditioned Hierarchical Flows for Spatiotemporal Events](https://mlsanity.com/paper/2605.01226/) (2026)

## Abstract (arXiv)

High-order interaction events are common in real-world applications. Learning embeddings that encode the complex relationships of the participants from these events is of great importance in knowledge mining and predictive tasks. Despite the success of existing approaches, e.g. Poisson tensor factorization, they ignore the sparse structure underlying the data, namely the occurred interactions are far less than the possible interactions among all the participants. In this paper, we propose Nonparametric Embeddings of Sparse High-order interaction events (NESH). We hybridize a sparse hypergraph (tensor) process and a matrix Gaussian process to capture both the asymptotic structural sparsity within the interactions and nonlinear temporal relationships between the participants. We prove strong asymptotic bounds (including both a lower and an upper bound) of the sparsity ratio, which reveals the asymptotic properties of the sampled structure. We use batch-normalization, stick-breaking construction, and sparse variational GP approximations to develop an efficient, scalable model inference algorithm. We demonstrate the advantage of our approach in several real-world applications.