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Exact Selective Inference for Spectral Clustering via Piecewise-Constant Graph Perturbation — arXiv:2611.04995

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.04995
License (as archived): CC0-1.0
Archived: 2026-11-04T21:51:50.767Z
SHA-256 of the archived text: 1b4fa5b7b742bafde0c7092b165e7002798bc20cf0208637964416944b8d0b8e
Stable URL of this page: https://metraipolis.com/documento/dc_7bb0c3da7cdf

How to cite

Exact Selective Inference for Spectral Clustering via Piecewise-Constant Graph Perturbation — arXiv:2611.04995 — arXiv (en), https://arxiv.org/abs/2611.04995 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7bb0c3da7cdf (Metraipolis archive dc_7bb0c3da7cdf, sha256 1b4fa5b7b742bafde0c7092b165e7002798bc20cf0208637964416944b8d0b8e)

BibTeX

@misc{dc7bb0c3da7cdf,
  title = {Exact Selective Inference for Spectral Clustering via Piecewise-Constant Graph Perturbation — arXiv:2611.04995},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.04995},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7bb0c3da7cdf; sha256 1b4fa5b7b742bafde0c7092b165e7002798bc20cf0208637964416944b8d0b8e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.04995. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Cluster labels are often used twice: first to discover groups, and then to test whether the discovered groups differ. This double use of the data makes ordinary two-sample $p$-values anti-conservative. Selective inference fixes this by conditioning on the clustering event, but for spectral clustering the event appears difficult because the algorithm combines an affinity map, an eigendecomposition, and a rounding step. We show that, for spectral clustering based on unweighted $\varepsilon$- or $k$-nearest-neighbor graphs, the obstruction is the affinity construction rather than the eigendecomposition. Along the one-dimensional perturbation used by the truncated-$\chi$ selective test, graph changes occur only at finitely many real roots of data-dependent quadratic distance comparisons. Between these breakpoints, the graph, Laplacian spectrum, embedding, rounding, and reported cluster pair are deterministic functions of a finite graph state. Consequently, in real arithmetic and under a known-scale spherical Gaussian model, the selection set is an exact finite union of intervals, yielding finite-sample selective $p$-values for selected spectral-cluster pairs. The same argument gives feature-wise truncated-normal tests. We also record direct extensions to known feature covariance, eigengap-selected $K$, and auxiliary-coordinate graphs. We validate null and partial-null calibration, operational power, numerical sensitivity, and model-scope diagnostics, and give a working-model PBMC algorithmic illustration. Smooth kernels such as RBF affinities fall outside the finite-state guarantee.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG) ; Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2611.04995 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T21:38:49.741Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).