{"paper":{"title":"Node-private community estimation in stochastic block models: Tractable algorithms and lower bounds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Consistent community recovery in stochastic block models is achievable under node differential privacy using new polynomial-time algorithms that require the privacy parameter epsilon to grow at a controlled rate.","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Ethan D'souza, Laurentiu Marchis, Po-Ling Loh, Tom\\'a\\v{s} Fl\\'idr","submitted_at":"2026-05-15T13:27:24Z","abstract_excerpt":"We study the classical problem of community recovery in stochastic block models with a fixed number of communities, with a twist: We seek algorithms that are stable with respect to node-wise changes in the graph structure, formally defined as a differential privacy constraint. The algorithms we develop are based on spectral clustering, where we introduce privacy to the community recovery pipeline in the form of directly privatizing the adjacency matrix; private PCA; private convex optimization; private low-rank matrix estimation; and private approximate subspace estimation. Straightforward app"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We develop novel algorithms based on (1) sampling from an exponential mechanism with a Lipschitz extension and (2) a general framework for constructing smooth projections from the space of undirected graphs to the space of bounded-degree graphs, which can then be combined with various edge-private algorithms. [...] We also develop novel lower bounds on the growth rate of ε required in order to achieve consistent community estimation under node privacy.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis assumes that the underlying stochastic block model parameters (edge probabilities within and between communities) are such that consistent community recovery is possible even in the non-private case; the privacy mechanisms are then shown to preserve this consistency provided ε grows sufficiently fast. This modeling choice is stated in the problem setup and is used to define the target accuracy level for the private estimators.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Develops tractable node-differentially private algorithms for community estimation in fixed-community stochastic block models together with lower bounds on the privacy parameter ε needed for consistency.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Consistent community recovery in stochastic block models is achievable under node differential privacy using new polynomial-time algorithms that require the privacy parameter epsilon to grow at a controlled rate.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"73e47bf276f3835c529cc66766b3958fb705d15f03e3da06295e232a2f31a46e"},"source":{"id":"2605.15943","kind":"arxiv","version":1},"verdict":{"id":"60832e0c-a77a-4cae-9376-930d0f8cf04b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:06:07.531719Z","strongest_claim":"We develop novel algorithms based on (1) sampling from an exponential mechanism with a Lipschitz extension and (2) a general framework for constructing smooth projections from the space of undirected graphs to the space of bounded-degree graphs, which can then be combined with various edge-private algorithms. [...] We also develop novel lower bounds on the growth rate of ε required in order to achieve consistent community estimation under node privacy.","one_line_summary":"Develops tractable node-differentially private algorithms for community estimation in fixed-community stochastic block models together with lower bounds on the privacy parameter ε needed for consistency.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analysis assumes that the underlying stochastic block model parameters (edge probabilities within and between communities) are such that consistent community recovery is possible even in the non-private case; the privacy mechanisms are then shown to preserve this consistency provided ε grows sufficiently fast. This modeling choice is stated in the problem setup and is used to define the target accuracy level for the private estimators.","pith_extraction_headline":"Consistent community recovery in stochastic block models is achievable under node differential privacy using new polynomial-time algorithms that require the privacy parameter epsilon to grow at a controlled rate."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15943/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.035276Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:12:07.755521Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:44.885742Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.723328Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ac45b2c542490b7a3a2a025f8a55c678d5835dce5783b4e6ad12a7ef090401fe"},"references":{"count":74,"sample":[{"doi":"","year":2018,"title":"E. Abbe. Community detection and stochastic block models: recent developments.Journal of Machine Learning Research, 18(177):1–86, 2018","work_id":"bcdc14ef-0f98-41f0-a1c6-066216c9008d","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"On Maximal Correlation, Hypercontractivity, and the Data Processing Inequality studied by Erkip and Cover","work_id":"468427fe-0bf9-4623-a5fa-5f6b9f99d089","ref_index":2,"cited_arxiv_id":"1304.6133","is_internal_anchor":true},{"doi":"","year":2021,"title":"Avella-Medina","work_id":"c9beaf3a-8215-4726-b312-b5c30543403b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2067,"title":"M. Avella-Medina, C. Bradshaw, and P. Loh. Differentially private inference via noisy optimization. The Annals of Statistics, 51(5):2067–2092, 2023","work_id":"c6f6c27c-abf8-433a-aa75-064431191d16","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"J. Blocki, A. Blum, A. Datta, and O. Sheffet. The Johnson-Lindenstrauss transform itself preserves differential privacy. In2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, pages 410","work_id":"30cbd78d-84e4-41b6-aac8-2ec41026b283","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":74,"snapshot_sha256":"3e155ab23b3407b12f37992c3dc13bc7a325e8eb6b321bddb6a67ff1f8ac8725","internal_anchors":6},"formal_canon":{"evidence_count":2,"snapshot_sha256":"22d8047770df651359ed60bdfcd182801e2c89bcd581d949ae93751065b22276"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}