# Graph Structure Learning with Interpretable Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2406.14786 · HTML: https://mlsanity.com/paper/2406.14786/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 54 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Builds on (most cited first, 29 of 29)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Do Bayesian Neural Networks Need To Be Fully Stochastic?](https://mlsanity.com/paper/2211.06291/) (2022)
- [Latent-Graph Learning for Disease Prediction](https://mlsanity.com/paper/2003.13620/) (2020)
- [Learning to Learn Graph Topologies](https://mlsanity.com/paper/2110.09807/) (2021)
- [Visualization in Bayesian workflow](https://mlsanity.com/paper/1709.01449/) (2017)
- [Learning Sparse Graphs Under Smoothness Prior](https://mlsanity.com/paper/1609.03448/) (2016)
- [GLAD: Learning Sparse Graph Recovery](https://mlsanity.com/paper/1906.00271/) (2019)
- [The prior can generally only be understood in the context of the likelihood](https://mlsanity.com/paper/1708.07487/) (2017)
- [Accelerated Graph Learning from Smooth Signals](https://mlsanity.com/paper/2110.09677/) (2021)
- [Conditional Variational Autoencoder for Learned Image Reconstruction](https://mlsanity.com/paper/2110.11681/) (2021)
- [Non-Parametric Graph Learning for Bayesian Graph Neural Networks](https://mlsanity.com/paper/2006.13335/) (2020)
- [Uncertainty Quantification for Deep Unrolling-Based Computational Imaging](https://mlsanity.com/paper/2207.00698/) (2022)
- [Bayesian inference of network structure from information cascades](https://mlsanity.com/paper/1908.03318/) (2019)
- [Quantifying Sources of Uncertainty in Deep Learning-Based Image Reconstruction](https://mlsanity.com/paper/2011.08413/) (2020)
- [Learning Graph Structure from Convolutional Mixtures](https://mlsanity.com/paper/2205.09575/) (2022)
- [Learning Sparse Graphs via Majorization-Minimization for Smooth Node Signals](https://mlsanity.com/paper/2202.02815/) (2022)
- [Bayesian topology inference on partially known networks from input-output pairs](https://mlsanity.com/paper/2309.06532/) (2023)
- [Bayesian Inference of Diffusion Networks with Unknown Infection Times](https://mlsanity.com/paper/1602.08114/) (2016)
- [Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo](https://mlsanity.com/paper/1604.00695/) (2016)

## Built on by (most cited first, 4 of 4)

- [Stabilizing the Kumaraswamy Distribution](https://mlsanity.com/paper/2410.00660/) (2024)
- [Online Proximal ADMM for Graph Learning from Streaming Smooth Signals](https://mlsanity.com/paper/2409.12916/) (2024)
- [LASE: Learned Adjacency Spectral Embeddings](https://mlsanity.com/paper/2412.17734/) (2024)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse problem with a smoothness promoting objective and rely on iterative methods to obtain a solution. In supervised settings where graph labels are available, one can unroll and truncate these iterations into a deep network that is trained end-to-end. Such a network is parameter efficient and inherits inductive bias from the optimization formulation, an appealing aspect for data constrained settings in, e.g., medicine, finance, and the natural sciences. But typically such settings care equally about uncertainty over edge predictions, not just point estimates. Here we introduce novel iterations with independently interpretable parameters, i.e., parameters whose values - independent of other parameters' settings - proportionally influence characteristics of the estimated graph, such as edge sparsity. After unrolling these iterations, prior knowledge over such graph characteristics shape prior distributions over these independently interpretable network parameters to yield a Bayesian neural network (BNN) capable of graph structure learning (GSL) from smooth signal observations. Fast execution and parameter efficiency allow for high-fidelity posterior approximation via Markov Chain Monte Carlo (MCMC) and thus uncertainty quantification on edge predictions. Synthetic and real data experiments corroborate this model's ability to provide well-calibrated estimates of uncertainty, in test cases that include unveiling economic sector modular structure from S&P500 data and recovering pairwise digit similarities from MNIST images. Overall, this framework enables GSL in modest-scale applications where uncertainty on the data structure is paramount.