Applied Math And Analysis Seminar
Wednesday, January 18, 2017, 12:00pm, 119 Physics
Alexander Cloninger (Yale University)
Incorporation of geometry into learning algorithms and medicine
Abstract:- This talk focuses on two instances in which scientific fields
outside mathematics benefit from incorporating the geometry of the data.
In each instance, the application area motivates the need for new
mathematical approaches and algorithms and leads to interesting new
questions. (1) A method to determine and predict drug treatment
effectiveness for patients based off their baseline information. This
motivates building a function adapted diffusion operator on
high-dimensional data X when the function F can only be evaluated on
large subsets of X, and defining a localized filtration of F and
estimation values of F at a finer scale than it is reliable naively.
(2) The current empirical success of deep learning in imaging and medical
applications, in which theory and understanding is lagging far behind.
By assuming the data lie near low-dimensional manifolds and building
local wavelet frames, we improve on existing theory that breaks down when
the ambient dimension is large (the regime in which deep learning has
seen the most success). [video]
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