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Research Seminar: Austin Warner and Yifan Chen, Department of Statistics
March 25, 2022 @ 11:30 AM – 1:00 PM CDT
Austin Warner: “CuSum for Sequential Change Diagnosis” , Joint work with G.Fellouris
The problem of sequential change diagnosis is considered, where a sequence of independent random elements is accessed sequentially. At some unknown time there is an abrupt change in its distribution, and there are two main operational goals: to quickly detect the change and to accurately identify the post-change distribution among a finite set of alternatives. We consider a standard change-point detection algorithm that raises an alarm as soon as the CuSum statistic that corresponds to one of the post-change alternatives exceeds a certain threshold. This procedure is shown to control the worst-case conditional probability of false isolation under some conditions, and at the same time minimize Lorden’s criterion for the detection delay, for every possible post-change distribution, to a first-order asymptotic approximation as both the worst-case probability of false isolation and the false alarm rate go to zero, but with the false alarm rate going to zero at a faster rate. Specifically, it is shown that these properties are satisfied under some conditions when the post-change distributions are more distant (in a Kullback-Leibler divergence sense) from one another than from the pre-change distribution.
Yifan Chen: “Accumulative Sketching for Nyström Methods and Nyström Methods for Attention Approximation ”
Nystrom methods are broadly applied to accelerate the computation involving kernel matrices, whose performance are mainly decided by the sketching matrices in use. We first propose a new framework to unify the common sub-sampling sketching and the gaussian sketching. We also explore how in general the Nystrom methods can be extended to the popular neural networks, transformers.
Technology Plaza, Suit 213 (Career Center)
616 E Green St. suite 213
Lunch RSVP Form (Please Fill the form by the end of Wednesday March 23th)