{"paper":{"title":"Estimating Precision Matrices for High-Dimensional Interval-Valued Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Assuming upper and lower interval bounds share the same dependency structure allows consistent estimation of precision matrices via a specialized graphical lasso.","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Hao Xu, Wan Tian, Wenhao Cui, Zhongfeng Qin","submitted_at":"2026-05-14T06:47:31Z","abstract_excerpt":"In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional methods often fall short when dealing with high-dimensional interval-valued data, where each observation is represented as an interval rather than a single point. This paper proposes a novel framework for estimating precision matrices in such contexts, addressing the unique challenges posed by the interval nature of the data. Specifically, we assume that the"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We assume that the upper and lower bounds of the intervals share the same conditional dependency structure, and then formulate the interval graphical lasso optimization objective to estimate the precision matrix. ... prove the sparsity and consistency of the estimator.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the upper and lower bounds of the intervals share the same conditional dependency structure.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces interval graphical lasso to estimate a shared precision matrix for interval-valued data and proves its sparsity and consistency.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Assuming upper and lower interval bounds share the same dependency structure allows consistent estimation of precision matrices via a specialized graphical lasso.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"97665accb7837c2825f4259920da6aad9105d9df888ca89e0f7d73c724b00440"},"source":{"id":"2605.14453","kind":"arxiv","version":1},"verdict":{"id":"14ea142c-51a4-4aa0-b0c7-9ac69a821210","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:57:17.072395Z","strongest_claim":"We assume that the upper and lower bounds of the intervals share the same conditional dependency structure, and then formulate the interval graphical lasso optimization objective to estimate the precision matrix. ... prove the sparsity and consistency of the estimator.","one_line_summary":"Introduces interval graphical lasso to estimate a shared precision matrix for interval-valued data and proves its sparsity and consistency.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the upper and lower bounds of the intervals share the same conditional dependency structure.","pith_extraction_headline":"Assuming upper and lower interval bounds share the same dependency structure allows consistent estimation of precision matrices via a specialized graphical lasso."},"references":{"count":129,"sample":[{"doi":"","year":2016,"title":"Essays in honor of Aman Ullah , volume=","work_id":"2f2ae1b3-bdf1-4c1d-821e-820c1c90befe","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/s0047-259x(03)00096-4","year":2004,"title":"A well-conditioned estimator for large-dimensional covariance matrices , volume =","work_id":"22bbe490-8f1d-4be8-984f-a7ae73cb490e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"Journal of the American Statistical Association , volume=","work_id":"2abde437-9563-4515-875d-c9ba0fc3f786","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Econometric Reviews , year=","work_id":"c4e0dce7-8f01-464c-b49b-f58edd7464c2","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"Journal of Business & Economic Statistics , volume=","work_id":"230921f1-e264-46cc-a5a4-23e338d54caa","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":129,"snapshot_sha256":"5a3ac7bd275070ca59ce9b1dabb16b1fb0f5803eeb9280bc2f32bd23c7cfc85b","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}