no code implementations • 8 Dec 2015 • Changbo Zhu, Huan Xu
In many problems in machine learning and operations research, we need to optimize a function whose input is a random variable or a probability density function, i. e. to solve optimization problems in an infinite dimensional space.
no code implementations • 8 Dec 2015 • Changbo Zhu, Huan Xu, Shuicheng Yan
With the success of modern internet based platform, such as Amazon Mechanical Turk, it is now normal to collect a large number of hand labeled samples from non-experts.
no code implementations • 6 Dec 2014 • Canyi Lu, Changbo Zhu, Chunyan Xu, Shuicheng Yan, Zhouchen Lin
This work studies the Generalized Singular Value Thresholding (GSVT) operator ${\text{Prox}}_{g}^{{\sigma}}(\cdot)$, \begin{equation*} {\text{Prox}}_{g}^{{\sigma}}(B)=\arg\min\limits_{X}\sum_{i=1}^{m}g(\sigma_{i}(X)) + \frac{1}{2}||X-B||_{F}^{2}, \end{equation*} associated with a nonconvex function $g$ defined on the singular values of $X$.
no code implementations • NeurIPS 2014 • Changbo Zhu, Huan Xu, Chenlei Leng, Shuicheng Yan
In this paper, we present theoretical analysis of SON~--~a convex optimization procedure for clustering using a sum-of-norms (SON) regularization recently proposed in \cite{ICML2011Hocking_419, SON, Lindsten650707, pelckmans2005convex}.