Probability density estimation for sets of large graphs with respect to spectral information using stochastic block models
This work addresses graph-valued data analysis for applications in network science, but it is incremental as it applies existing stochastic block models to a new spectral-based metric.
The paper tackles the problem of estimating probability densities for sets of large graphs by using spectral information, specifically the ℓ₂ norm between eigenvalues of adjacency matrices as a pseudo-metric, and approximates the true distribution μ with an inferred distribution μ̂, showing experimentally that complex distributions can be approximated well.
For graph-valued data sampled iid from a distribution $μ$, the sample moments are computed with respect to a choice of metric. In this work, we equip the set of graphs with the pseudo-metric defined by the $\ell_2$ norm between the eigenvalues of the respective adjacency matrices. We use this pseudo metric and the respective sample moments of a graph valued data set to infer the parameters of a distribution $\hatμ$ and interpret this distribution as an approximation of $μ$. We verify experimentally that complex distributions $μ$ can be approximated well taking this approach.