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Online Gradient Descent in Function Space
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.
Online Crowdsourcing
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.
Generalized Singular Value Thresholding
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 $X$.
Convex Optimization Procedure for Clustering: Theoretical Revisit
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}.
