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We prove that these methods enjoy, both with high probability and in expectation, a convergence rate of order 1\/<jats:italic>T<\/jats:italic> up to logarithmic factors on the objective function scale, where <jats:italic>T<\/jats:italic> denotes the number of iterations. The benefits of our new computational framework are demonstrated on both synthetic and real data, and our implementation is available in a github repository  (Log-Concave Computation).<\/jats:p>","DOI":"10.1007\/s12532-024-00252-0","type":"journal-article","created":{"date-parts":[[2024,4,30]],"date-time":"2024-04-30T17:01:49Z","timestamp":1714496509000},"page":"185-228","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A new computational framework for log-concave density estimation"],"prefix":"10.1007","volume":"16","author":[{"given":"Wenyu","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rahul","family":"Mazumder","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard J.","family":"Samworth","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,4,30]]},"reference":[{"issue":"58","key":"252_CR1","doi-asserted-by":"publisher","first-page":"3235","DOI":"10.1109\/TIT.2011.2182178","volume":"5","author":"A Agarwal","year":"2012","unstructured":"Agarwal, A., Bartlett, P.L., Ravikumar, P., Wainwright, M.J.: Information-theoretic lower bounds on the oracle complexity of stochastic convex optimization. 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