[Turing-Southampton] S3RI seminar: Yi Yu, Thursday 2-3pm

[Helen Ogden]

Dear all,

On Thursday (14 February) at 2pm in 54 / 7035 (7B), we have an S3RI 
seminar from Yi Yu (University of Bristol) on "Univariate Mean Change 
Point Detection: Penalization, CUSUM and Optimality". Details are given 
below.

The seminar will also be available via a live web-cast at
https://coursecast.soton.ac.uk/Panopto/Pages/Viewer.aspx?id=8b1c58e7-6289-4a89-90f9-a9f1008d9bc1

The talk will be followed by tea and cake in the staff reading room on 
level 4 of building 54.

All are welcome!

Best wishes,

Helen

Univariate Mean Change Point Detection: Penalization, CUSUM and Optimality

Yi Yu, University of Bristol

The problem of univariate mean change point detection and localization 
based on a sequence of n independent observations with piecewise 
constant means has been intensively studied for more than half century, 
and serves as a blueprint for change point problems in more complex 
settings. We provide a complete characterization of this classical 
problem in a general framework in which the upper bound on the noise 
variance $\sigma^2$, the minimal spacing ∆ between two consecutive 
change points and the minimal magnitude of the changes κ, are allowed to 
vary with n. We first show that consistent localization of the change 
points when the signal-to-noise ratio $\frac{\kappa 
\sqrt{\Delta}}{\sigma}$ is uniformly bounded from above is impossible. 
In contrast, when $\frac{\kappa \sqrt{\Delta}}{\sigma}$ is diverging in 
$n$ at any arbitrary slow rate, we demonstrate that two 
computationally-efficient change point estimators, one based on the 
solution to an $\ell_0$-penalized least squares problem and the other on 
the popular WBS algorithm, are both consistent and achieve a 
localization rate of the order $\frac{\sigma^2}{\kappa^2} \log(n)$. We 
further show that such rate is minimax optimal, up to a log(n) term.

https://arxiv.org/abs/1810.09498


For the current schedule of S3RI seminars, see 
https://tinyurl.com/s3riseminar

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