{"doi":"10.1137/19m126476x","title":"ISLET: Fast and Optimal Low-Rank Tensor Regression via Importance Sketching","abstract":"In this paper, we develop a novel procedure for low-rank tensor regression, namely Importance Sketching Low-rank Estimation for Tensors (ISLET). The central idea behind ISLET is importance sketching, i.e., carefully designed sketches based on both the responses and low-dimensional structure of the parameter of interest. We show that the proposed method is sharply minimax optimal in terms of the mean-squared error under low-rank Tucker assumptions and under the randomized Gaussian ensemble design. In addition, if a tensor is low-rank with group sparsity, our procedure also achieves minimax optimality. Further, we show through numerical study that ISLET achieves comparable or better mean-squared error performance to existing state-of-the-art methods while having substantial storage and run-time advantages including capabilities for parallel and distributed computing. In particular, our procedure performs reliable estimation with tensors of dimension $p = O(10^8)$ and is 1 or 2 orders of magnitude faster than baseline methods.","journal":"SIAM Journal on Mathematics of Data Science","year":2020,"id":91427,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":45,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9492,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2020-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":457650,"name":"Yuetian Luo","orcid":"0000-0001-5145-3868","position":1,"is_corresponding":false},{"id":325783,"name":"Garvesh Raskutti","orcid":"0000-0002-0522-5423","position":2,"is_corresponding":false},{"id":60581,"name":"Ming Yuan","orcid":"0000-0002-4415-8606","position":3,"is_corresponding":false},{"id":392362,"name":"Anru R. Zhang","orcid":"0000-0002-8721-5252","position":0,"is_corresponding":true}],"reference_count":110,"raw_metadata":null,"created_at":"2026-07-18T22:28:45.409789Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}