# Conditional Uncertainty Quantification for Tensorized Topological Neural Networks

arXiv: https://arxiv.org/abs/2410.15241 · HTML: https://mlsanity.com/paper/2410.15241/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 73 references that are in the map.
- First posted on arXiv 20 Oct 2024.

## Builds on (most cited first, 30 of 48)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [On the Expressive Power of Deep Learning: A Tensor Analysis](https://mlsanity.com/paper/1509.05009/) (2015)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecasting](https://mlsanity.com/paper/2105.04100/) (2021)
- [Tensor SVD: Statistical and Computational Limits](https://mlsanity.com/paper/1703.02724/) (2017)
- [Graph-based Asynchronous Event Processing for Rapid Object Recognition](https://mlsanity.com/paper/2308.14419/) (2023)
- [Tensor Regression Networks](https://mlsanity.com/paper/1707.08308/) (2017)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [Persistence Homology of Networks: Methods and Applications](https://mlsanity.com/paper/1907.08708/) (2019)
- [Tensor Clustering with Planted Structures: Statistical Optimality and Computational Limits](https://mlsanity.com/paper/2005.10743/) (2020)
- [Uncertainty Quantification for Traffic Forecasting: A Unified Approach](https://mlsanity.com/paper/2208.05875/) (2022)

## Built on by (most cited first, 3 of 3)

- [TEAFormers: TEnsor-Augmented Transformers for Multi-Dimensional Time Series Forecasting](https://mlsanity.com/paper/2410.20439/) (2024)
- [ACT-Tensor: Tensor Completion Framework for Financial Dataset Imputation](https://mlsanity.com/paper/2508.01861/) (2025)
- [Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection](https://mlsanity.com/paper/2605.19122/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have become the de facto standard for analyzing graph-structured data, leveraging message-passing techniques to capture both structural and node feature information. However, recent studies have raised concerns about the statistical reliability of uncertainty estimates produced by GNNs. This paper addresses this crucial challenge by introducing a novel technique for quantifying uncertainty in non-exchangeable graph-structured data, while simultaneously reducing the size of label prediction sets in graph classification tasks. We propose Conformalized Tensor-based Topological Neural Networks (CF-T2NN), a new approach for rigorous prediction inference over graphs. CF-T2NN employs tensor decomposition and topological knowledge learning to navigate and interpret the inherent uncertainty in decision-making processes. This method enables a more nuanced understanding and handling of prediction uncertainties, enhancing the reliability and interpretability of neural network outcomes. Our empirical validation, conducted across 10 real-world datasets, demonstrates the superiority of CF-T2NN over a wide array of state-of-the-art methods on various graph benchmarks. This work not only enhances the GNN framework with robust uncertainty quantification capabilities but also sets a new standard for reliability and precision in graph-structured data analysis.