{"paper":{"title":"Adaptive Kernel Density Estimation with Pre-training","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A pre-trained neural network can recommend location-adaptive kernels to achieve efficient density estimation in high dimensions.","cross_cats":["cs.LG","stat.ME"],"primary_cat":"stat.ML","authors_text":"Ke Deng, Ruitong Zhang","submitted_at":"2026-05-13T07:03:54Z","abstract_excerpt":"Density estimation in high-dimensional settings is an important and challenging statistical problem.Traditional methods based on kernel smoothing are inefficient in high dimensions due to the difficulties in specifying appropriate location-adaptive kernels. In this work, we introduce pre-training, a key idea behind many cutting-edge AI technologies, to the context of non-parametric density estimation. By establishing a pre-trained neural network that can recommend an appropriate location-adaptive kernel for each sample point, efficient density estimation with adaptive kernels is achieved in hi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By establishing a pre-trained neural network that can recommend an appropriate location-adaptive kernel for each sample point, efficient density estimation with adaptive kernels is achieved in high dimensions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The target distribution is sufficiently close to the pre-training distribution family (or can be made so via fine-tuning) and that the neural network reliably recommends kernels that improve estimation accuracy.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A pre-trained neural network selects adaptive kernels per sample point to enable accurate high-dimensional kernel density estimation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A pre-trained neural network can recommend location-adaptive kernels to achieve efficient density estimation in high dimensions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b3eaf8a6ad9929846446e5bb43895fdedd450598f521f89b0491f9fdafe0b46f"},"source":{"id":"2605.13092","kind":"arxiv","version":1},"verdict":{"id":"294e3e74-3593-4262-92f8-f6178db5b5f7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:28:34.473707Z","strongest_claim":"By establishing a pre-trained neural network that can recommend an appropriate location-adaptive kernel for each sample point, efficient density estimation with adaptive kernels is achieved in high dimensions.","one_line_summary":"A pre-trained neural network selects adaptive kernels per sample point to enable accurate high-dimensional kernel density estimation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The target distribution is sufficiently close to the pre-training distribution family (or can be made so via fine-tuning) and that the neural network reliably recommends kernels that improve estimation accuracy.","pith_extraction_headline":"A pre-trained neural network can recommend location-adaptive kernels to achieve efficient density estimation in high dimensions."},"references":{"count":35,"sample":[{"doi":"","year":1994,"title":"1994 , edition =","work_id":"6cb55bed-c071-4192-9c4b-d8f565e56424","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"2016 , publisher =","work_id":"a57269a6-e3b3-4082-8f00-14f5db83900b","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The Annals of Mathematical Statistics , year =","work_id":"e871f4cb-4428-4ff5-a0fd-93f42029006a","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The Annals of Mathematical Statistics , year =","work_id":"0b5f2a2d-7106-4fea-bf9f-79f01bb7744e","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1990,"title":"1990 , series =","work_id":"c1586e17-4167-42d0-b72d-9240640b76b3","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":35,"snapshot_sha256":"8ab4c1106ea83cd76563185c8bbf1ad0f54d5d1eebaf5576e247f4f62f1a2278","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"}