{"type":"conference","title":"Mean estimation in high-dimensional binary Markov Gaussian mixture models","intvolume":"        35","citation":{"mla":"Zhang, Yihan, and Nir Weinberger. “Mean Estimation in High-Dimensional Binary Markov Gaussian Mixture Models.” <i>36th Conference on Neural Information Processing Systems</i>, vol. 35, ML Research Press, 2022.","chicago":"Zhang, Yihan, and Nir Weinberger. “Mean Estimation in High-Dimensional Binary Markov Gaussian Mixture Models.” In <i>36th Conference on Neural Information Processing Systems</i>, Vol. 35. ML Research Press, 2022.","short":"Y. Zhang, N. Weinberger, in:, 36th Conference on Neural Information Processing Systems, ML Research Press, 2022.","ista":"Zhang Y, Weinberger N. 2022. Mean estimation in high-dimensional binary Markov Gaussian mixture models. 36th Conference on Neural Information Processing Systems. NeurIPS: Neural Information Processing Systems, NeurIPS, vol. 35.","ieee":"Y. Zhang and N. Weinberger, “Mean estimation in high-dimensional binary Markov Gaussian mixture models,” in <i>36th Conference on Neural Information Processing Systems</i>, New Orleans, LA, United States, 2022, vol. 35.","apa":"Zhang, Y., &#38; Weinberger, N. (2022). Mean estimation in high-dimensional binary Markov Gaussian mixture models. In <i>36th Conference on Neural Information Processing Systems</i> (Vol. 35). New Orleans, LA, United States: ML Research Press.","ama":"Zhang Y, Weinberger N. Mean estimation in high-dimensional binary Markov Gaussian mixture models. In: <i>36th Conference on Neural Information Processing Systems</i>. Vol 35. ML Research Press; 2022."},"conference":{"name":"NeurIPS: Neural Information Processing Systems","location":"New Orleans, LA, United States","start_date":"2022-11-28","end_date":"2022-12-09"},"alternative_title":["NeurIPS"],"acknowledgement":"Part of this work was done when YZ was a postdoc at Technion where he received funding from\r\nthe European Union’s Horizon 2020 research and innovation programme under grant agreement No 682203-ERC-[Inf-Speed-Tradeoff]. The work of of NW was supported in part by the Israel Science Foundation (ISF) under Grant 1782/22. NW is grateful to Guy Bresler for introducing him to this problem, for the initial ideas that led to this research, and for many helpful discussions on the topic.","corr_author":"1","date_updated":"2024-08-05T09:48:58Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":35,"file_date_updated":"2024-08-05T09:44:49Z","year":"2022","department":[{"_id":"MaMo"}],"abstract":[{"text":"We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an estimator observes n samples of a d-dimensional parameter vector θ∗∈Rd, multiplied by a random sign Si (1≤i≤n), and corrupted by isotropic standard Gaussian noise. The sequence of signs {Si}i∈[n]∈{−1,1}n is drawn from a stationary homogeneous Markov chain with flip probability δ∈[0,1/2]. As δ varies, this model smoothly interpolates two well-studied models: the Gaussian Location Model for which δ=0 and the Gaussian Mixture Model for which δ=1/2. Assuming that the estimator knows δ, we establish a nearly minimax optimal (up to logarithmic factors) estimation error rate, as a function of ∥θ∗∥,δ,d,n. We then provide an upper bound to the case of estimating δ, assuming a (possibly inaccurate) knowledge of θ∗. The bound is proved to be tight when θ∗ is an accurately known constant. These results are then combined to an algorithm which estimates θ∗ with δ unknown a priori, and theoretical guarantees on its error are stated.","lang":"eng"}],"quality_controlled":"1","language":[{"iso":"eng"}],"external_id":{"arxiv":["2206.02455"]},"date_created":"2024-05-29T06:37:16Z","ddc":["000"],"scopus_import":"1","_id":"17086","publication":"36th Conference on Neural Information Processing Systems","day":"01","status":"public","article_processing_charge":"No","has_accepted_license":"1","date_published":"2022-12-01T00:00:00Z","publication_status":"published","publication_identifier":{"isbn":["9781713871088"]},"month":"12","oa_version":"Published Version","author":[{"last_name":"Zhang","first_name":"Yihan","full_name":"Zhang, Yihan","id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","orcid":"0000-0002-6465-6258"},{"last_name":"Weinberger","first_name":"Nir","full_name":"Weinberger, Nir"}],"file":[{"relation":"main_file","date_updated":"2024-08-05T09:44:49Z","file_name":"2022_NeurIPS_Zhang.pdf","file_id":"17392","file_size":476307,"content_type":"application/pdf","date_created":"2024-08-05T09:44:49Z","success":1,"checksum":"05f6f9f8fc34e224e0cad045b9489030","creator":"dernst","access_level":"open_access"}],"publisher":"ML Research Press"}