Papers › Bias-Variance Tradeoffs in Joint Spectral Embeddings
Bias-Variance Tradeoffs in Joint Spectral Embeddings
Benjamin Draves, Daniel L. Sussman
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Joint spectral embeddings facilitate analysis of multiple network data by simultaneously mapping vertices in each network to points in Euclidean space where statistical inference is then performed. In this work, we consider one such joint embedding technique, the omnibus embedding of arXiv:1705.09355 , which has been successfully used for community detection, anomaly detection, and hypothesis testing tasks. To date the theoretical properties of this method have only been established under the strong assumption that the networks are conditionally i.i.d. random dot product graphs. Herein, we take a first step in characterizing the theoretical properties of the omnibus embedding in the presence of heterogeneous network data. Under a latent position model, we show the omnibus embedding implicitly regularizes its latent position estimates which induces a finite-sample bias-variance tradeoff for latent position estimation. We establish an explicit bias expression, derive a uniform concentration bound on the residual, and prove a central limit theorem characterizing the distributional properties of these estimates. These explicit bias and variance expressions enable us to state sufficient conditions for exact recovery in community detection tasks and develop a pivotal test statistic to determine whether two graphs share the same set of latent positions; demonstrating that accurate inference is achievable despite the estimator's inconsistency. These results are demonstrated in several experimental settings where statistical procedures utilizing the omnibus embedding are competitive, and oftentimes preferable, to comparable embedding techniques. These observations accentuate the viability of the omnibus embedding for multiple graph inference beyond the homogeneous network setting.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections