# Estimation of the Sample Frechet Mean: A Convolutional Neural Network Approach

arXiv: https://arxiv.org/abs/2210.07401 · HTML: https://mlsanity.com/paper/2210.07401/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 56 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
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- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Wasserstein Embedding for Graph Learning](https://mlsanity.com/paper/2006.09430/) (2020)
- [Metrics for Graph Comparison: A Practitioner's Guide](https://mlsanity.com/paper/1904.07414/) (2019)
- [A Consistent Histogram Estimator for Exchangeable Graph Models](https://mlsanity.com/paper/1402.1888/) (2014)
- [Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2202.03813/) (2022)
- [Network histograms and universality of blockmodel approximation](https://mlsanity.com/paper/1312.5306/) (2013)
- [Hypothesis Testing For Network Data in Functional Neuroimaging](https://mlsanity.com/paper/1407.5525/) (2014)
- [Discrete Wasserstein Barycenters: Optimal Transport for Discrete Data](https://mlsanity.com/paper/1507.07218/) (2015)
- [Modeling Network Populations via Graph Distances](https://mlsanity.com/paper/1904.07367/) (2019)
- [Randomised Wasserstein Barycenter Computation: Resampling with Statistical Guarantees](https://mlsanity.com/paper/2012.06397/) (2020)
- [Fr'echet Change Point Detection](https://mlsanity.com/paper/1911.11864/) (2019)
- [Network Recovery from Unlabeled Noisy Samples](https://mlsanity.com/paper/2104.14952/) (2021)
- [node2coords: Graph Representation Learning with Wasserstein Barycenters](https://mlsanity.com/paper/2007.16056/) (2020)
- [Theoretical analysis and computation of the sample Frechet mean for sets of large graphs based on spectral information](https://mlsanity.com/paper/2201.05923/) (2022)
- [An iterative step-function estimator for graphons](https://mlsanity.com/paper/1412.2129/) (2014)
- [Distributed Cartesian Power Graph Segmentation for Graphon Estimation](https://mlsanity.com/paper/1805.09978/) (2018)
- [Hausdorff and Wasserstein metrics on graphs and other structured data](https://mlsanity.com/paper/1907.00257/) (2019)

## Abstract (arXiv)

This work addresses the rising demand for novel tools in statistical and machine learning for "graph-valued random variables" by proposing a fast algorithm to compute the sample Frechet mean, which replaces the concept of sample mean for graphs (or networks). We use convolutional neural networks to learn the morphology of the graphs in a set of graphs. Our experiments on several ensembles of random graphs demonstrate that our method can reliably recover the sample Frechet mean.