42 open problems in mathematics
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: 42 open problems in mathematics
42 open problems in mathematics
https://khothuvien.cori!Ten Lectures and Forty-Two open Problems in the Mathematics of Data ScienceAfonso s. BandeiraDecember, 2015PrefaceThese arc no 42 open problems in mathematics otes from a course I gave at MIT on t he Fall of 2015 entitled: “18.S096: Topics in Mathematics of Data Science”. These notes are not in final form and will be continuously edited and/or corrected (as I am sure they contain many typos). Please use at your own risk and do let me know if you find any 42 open problems in mathematics typo/mistake.Part of t he content of t his course is greatly inspired by a course 1 took from Amit Singer while a graduate student at Princeton. Amit’42 open problems in mathematics
s course was inspiring and influential on my research interests. 1 can only hope that, those notes may one day inspire someone's research in the same https://khothuvien.cori!Ten Lectures and Forty-Two open Problems in the Mathematics of Data ScienceAfonso s. BandeiraDecember, 2015PrefaceThese arc no 42 open problems in mathematics solved [MS15]!).This list of problems does not necessarily contain the most important problems in the field (although some will be rat her important). 1 have tried to select a mix of important., perhaps approachable, and fun problems. Hopefully you will enjoy thinking about these problems as much as 42 open problems in mathematics 1 do!1would like to thank all t he students who took my course, it. was a great and interact ive audience' 1 would also like to thank Nicolas Boumal,42 open problems in mathematics
Ludwig Schmidt, and Jonathan Weed for letting me know of several typos. Thank you also to Nicolas Boumal, Dustin G. Mixon, Bernat Guillen Pegucrolcs,https://khothuvien.cori!Ten Lectures and Forty-Two open Problems in the Mathematics of Data ScienceAfonso s. BandeiraDecember, 2015PrefaceThese arc no 42 open problems in mathematics ................. 40.2 A couple of open Problems............................................................. 60.2.1Koinlós Conjecture............................................................. 60.2.2Matrix AM-GM inequality ...................................................... 70.3 Brief Review o 42 open problems in mathematics f some linear algebra tools............................................. 70.3.1Singular Value Decomposition...........................................42 open problems in mathematics
........ 70.3.2Spectral Dcconi|>osition...................................................... 810.3.3 Trace and norm..................................https://khothuvien.cori!Ten Lectures and Forty-Two open Problems in the Mathematics of Data ScienceAfonso s. BandeiraDecember, 2015PrefaceThese arc no 42 open problems in mathematics High Dimensions and the Spike Model101.1Dimension Reduction and PCA...................................................... 101.1.1PCA as best d-dimensional affine fit...................................... 101.1.2PCA as d-dimcnsional projection that preserves t he most variance......... 121.1.3Finding 42 open problems in mathematics the Principal Components.......................................... 131.1.4Which d should we pick? ..................................................42 open problems in mathematics
131.1.5A related open problem.................................................... 141.2PCA in high dimensions ami Marccnko-Pastur ....................https://khothuvien.cori!Ten Lectures and Forty-Two open Problems in the Mathematics of Data ScienceAfonso s. BandeiraDecember, 2015PrefaceThese arc no 42 open problems in mathematics ..................................... 181.3.1A brief mention of Wigner matrices ....................................... 221.3.2An open problem about spike models ....................................... 232Graphs, Diffusion Maps, and Semi-supervised Learning242.1Graphs................................ 42 open problems in mathematics ........................................... 242.1.1Cliques and Ramsey numbers................................................ 252.2Diffusion Maps.....42 open problems in mathematics
.............................................................. 292.2.1A coupleof examples..................................................... 32https://khothuvien.cori!Ten Lectures and Forty-Two open Problems in the Mathematics of Data ScienceAfonso s. BandeiraDecember, 2015PrefaceThese arc nohttps://khothuvien.cori!Ten Lectures and Forty-Two open Problems in the Mathematics of Data ScienceAfonso s. BandeiraDecember, 2015PrefaceThese arc noGọi ngay
Chat zalo
Facebook