[Colloquium] REMINDER: 7/15 TTIC Colloquium: Yuan Yao, Peking University (NOTE UNUSUAL DAY)

[Mary Marre]

> When:     Wednesday, July 15th at 11:00 a.m. (note unusual day)
>
> Where:    TTIC, 6045 S Kenwood Avenue, 5th Floor, Room 526
>
> Who:       Yuan Yao, Peking University
>
> Title:        Sparse Recovery via Dynamics
>
> Abstract: In this talk, we recover sparse signals from their noisy linear
> measurements by solving nonlinear differential equations (inclusions),
> which is based on the notion of inverse scale space (ISS) developed in
> applied mathematics. Our goal here is to bring this idea to address a
> challenging problem in statistics, \emph{i.e.} finding unbiased and
> sign-consistent estimators using dynamics. We call our dynamics
> \emph{Bregman ISS} and \emph{Linearized Bregman ISS}. A well-known
> shortcoming of LASSO and any convex regularization approaches lies in the
> bias of estimators. However, we show that under proper conditions, there
> exists a bias-free and sign-consistent point on the solution paths of such
> dynamics, which corresponds to a signal that is the unbiased estimate of
> the true signal and whose entries have the same signs as those of the true
> signs, \emph{i.e.} the oracle estimator. Therefore, their solution paths
> are regularization paths better than the LASSO regularization path, since
> the points on the latter path are biased when sign-consistency is reached.
> We also show how to efficiently compute their solution paths in both
> continuous and discretized settings: the full solution paths can be exactly
> computed piece by piece, and a discretization leads to \emph{Linearized
> Bregman iteration}, which is a simple iterative thresholding rule and easy
> to parallelize. Theoretical guarantees such as sign-consistency and minimax
> optimal $l_2$-error bounds are established in both continuous and discrete
> settings for specific points on the paths. Early-stopping rules for
> identifying these points are given. The key treatment relies on the
> development of differential inequalities for differential inclusions and
> their discretizations, which extends the previous results and leads to
> exponentially fast recovering of sparse signals before selecting wrong ones.
>
>
> This is a joint work with Feng Ruan (Stanford), Jiechao Xiong (PKU),
> Stanley Osher and Wotao Yin (UCLA).
>
>
> Host:  *Jinbo Xu*
>
>
>
>
>
> Mary C. Marre
> Administrative Assistant
> *Toyota Technological Institute*
> *6045 S. Kenwood Avenue*
> *Room 504*
> *Chicago, IL  60637*
> *p:(773) 834-1757 <%28773%29%20834-1757>*
> *f: (773) 357-6970 <%28773%29%20357-6970>*
> *mmarre at ttic.edu <mmarre at ttic.edu>*
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://mailman.cs.uchicago.edu/pipermail/colloquium/attachments/20150715/8824961f/attachment.htm