Recover Reco verin ing S Struct cture o e of N Nois isy D y - PowerPoint PPT Presentation

<latexit sha1_base64="eoT9fUNONOVctfMx8r4ZqaSHXDQ=">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</latexit> 2020 IEEE International Symposium on Information Theory Recover Reco verin ing S Struct cture o e of N Nois isy D y Data thro throug ugh h Hypo pothe thesis Te Testi ting ng Minoh Jeong ? , Alex Dytso † , Martina Cardone ? , and H. Vincent Poor † ? University of Minnesota † Princeton University The work of M. Jeong and M. Cardone was supported in part by the U.S. National Science Foundation under Grant CCF-1849757. 1 The work of A. Dytso and H. V. Poor was supported in part by the U.S. National Science Foundation under Grant CCF-1908308.

Motivation The problem of re recoveri ring ng da data struc ructure ure is becoming a prevailing task of modern communication and computing systems. 2

Motivation - Example The problem of re recoveri ring ng da data struc ructure ure is becoming a prevailing task of modern communication and computing systems. Pe Persona nal Noi Noise da data ta Privatizing personal data User • Recommender system Recommendation based on noisy data 3

Related Work ● Linear regression with shuffled data ○ A. Pananjady, M. J. Wainwright, and T. A. Courtade, “Linear regression with shuffled data: Statistical and computational limits of permutation recovery,” IEEE Transactions on Information Theory , vol. 64, no. 5, pp. 3286–3300, May 2018. ○ D. Hsu, K. Shi, and X. Sun, “Linear regression without correspondence,” in Proceedings of the 31st International Conference on Neural Information Processing Systems (NIPS), December 2017, pp. 1530–1539. ● Unlabeled sensing ○ J. Unnikrishnan, S. Haghighatshoar, and M. Vetterli, “Unlabeled sensing with random linear measurements,” IEEE Transactions on Information Theory , vol. 64, no. 5, pp. 3237–3253, May 2018. ○ S. Haghighatshoar and G. Caire, “Signal recovery from unlabeled samples,” IEEE Transactions on Signal Processing , vol. 66, no. 5, pp. 1242–1257, March 2018. 4

<latexit sha1_base64="WeHOTqpqZQB0bPSfG/Vf0l1Hb8=">AB/XicbVC7SgNBFL3rM8bX+uhsBoNgIWE3FopVwMZGiGAekCxhdnI3GTI7u8zMCjEf8XGQhFb/8POv3HyKDTxwMDhnHuZe06YCq6N5307S8srq2vruY385tb2zq67t1/TSaYVlkiEtUIqUbBJVYNwIbqUIahwLrYf967NcfUGmeyHszSDGIaVfyiDNqrNR2D1thRG4pl6TDowgVSoZXbfgFb0JyCLxZ6QAM1Ta7lerk7AsRmYoFo3fS81wZAqw5nAUb6VaUwp69MuNi2VNEYdDCfXj8iJVTokSpR90pCJ+ntjSGOtB3FoJ2NqenreG4v/ec3MRJfBkMs0MzbW9KMoE8QkZFyFTayQGTGwhDLF7a2E9aizNjC8rYEfz7yIqmViv5sXRXKpTPZnXk4AiO4R8uIAy3EAFqsDgEZ7hFd6cJ+fFeXc+pqNLzmznAP7A+fwBheWUjQ=</latexit> <latexit sha1_base64="Z5W/Dea9LIMl7risx9oLKryZr2A=">ACK3icbVC7TgMxEPTxJrwClDQWERJVdBcKBE0lCARQEqiaM+3Ryx8tmXvgaKI/6HhVyig4CFa/gMnpOC12mI0s6udndQq6SmOX6OJyanpmdm5+crC4tLySnV17cyb0glsCqOMu0jBo5IamyRJ4YV1CEWq8Dy9Ohzq59fovDT6lPoWOwVcaplLARSobvWgrY3UGWqHEAfvQTNbZi3KEheI7+R1OPWSeN4Ftw4mZbDR6aesgzIOhWa3E9HhX/C5IxqLFxHXerj+3MiLIR4UC71tJbKkzAEdSKLytEuPFsQVXGIrQA0F+s5g9Ost3wpMxvPgJzea+Ij9vjGAwvt+kYbJAqjnf2tD8j+tVK+1xlIbUtCLb4O5aXiZPgwuPC+C5mofgAgnAxeueiBA0EhrkoIfn98l9w1qgnO/XGSaO23xjHMc2CbZgnbZfvsiB2zJhPsj2wZ/YS3UdP0Vv0/jU6EY131tmPij4+AZLfqGw=</latexit> Related Work ● Linear regression with shuffled data ○ A. Pananjady, M. J. Wainwright, and T. A. Courtade, “Linear regression with shuffled data: Statistical and computational limits of permutation recovery,” IEEE Transactions on Information Theory , vol. 64, no. 5, pp. 3286–3300, May 2018. ○ D. Hsu, K. Shi, and X. Sun, “Linear regression without correspondence,” in Proceedings of the 31st International Conference on Neural Information Processing Systems (NIPS), December 2017, pp. 1530–1539. Main di ff erence: Bayesian perspective with prior distribution on the data ● Unlabeled sensing ○ J. Unnikrishnan, S. Haghighatshoar, and M. Vetterli, “Unlabeled sensing with random linear measurements,” IEEE Transactions on Information Theory , vol. 64, no. 5, pp. 3237–3253, May 2018. ○ S. Haghighatshoar and G. Caire, “Signal recovery from unlabeled samples,” IEEE Transactions on Signal Processing , vol. 66, no. 5, pp. 1242–1257, March 2018. 5