BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Learning with latent symmetries - Subhro Ghosh\, National Universi ty of Singapore DTSTART:20240531T130000Z DTEND:20240531T140000Z UID:TALK213472@talks.cam.ac.uk CONTACT:Dr Sergio Bacallado DESCRIPTION:Learning problems augmented with latent symmetries have attrac ted considerable interest in recent years. A significant class of such pro blems arises in experiments where a system is constrained to evolve in acc ordance with the rigid laws of nature\, such as the celebrated technique o f cryo electron microscopy (Cryo-EM). The constraint of such latent symmet ries\, given by group invariances or equivariances\, precludes the possibi lity of having many repeated measurements of the exact same object\, and p oses a fundamental challenge for learning a signal in the presence of ambi ent noise. We will start with a gentle introduction to the problem of lear ning under latent symmetries\, and explore its intriguing connections with a range of disparate topics — invariant theory\, harmonic analysis\, co mpressive sensing and Gaussian calculus. We will subsequently specialise t o the Multi Reference Alignment (MRA) model\, and explore the fundamental aspects of the recovery problem (such as sample complexity) in the presenc e of structural constraints on the signal (such as sparsity). In particula r\, we unveil a novel quartic dependence on noise level for the sample com plexity of sparse MRA\, leveraging a range of mathematical tools from unce rtainty principles of Fourier analysis to techniques from combinatorial op timisation.\n\nBased in part on the following works :\n\n[1] Sparse Multi- Reference Alignment: Phase Retrieval\, Uniform Uncertainty Principles and the Beltway Problem\, S. Ghosh and P. Rigollet\, Foundations of Computatio nal Mathematics\, 23(5)\, pp.1851-1898 (2023)\n\n[2] Minimax-optimal estim ation for sparse multi-reference alignment with collision-free signals\, S . Ghosh\, S.S. Mukherjee\, J.B. Pan\, arXiv preprint LOCATION:MR12\, Centre for Mathematical Sciences END:VEVENT END:VCALENDAR