arXiv subjects

Chao Qu

Publications and source records attributed to Chao Qu.

57 records · Page 4Linked to original sources

arXiv2017

Linear convergence of SDCA in statistical estimation

In this paper, we consider stochastic dual coordinate (SDCA) {\em without} strongly convex assumption or convex assumption. We show that SDCA converges linearly under mild conditions termed restricted strong convexity. This covers a wide array of popular statistical models including Lasso, group Lasso, and logistic regression with $\ell_1$ regularization, corrected Lasso and linear regression with SCAD regularizer. This significantly improves previous convergence results on SDCA for problems that are not strongly convex. As a by product, we derive a dual free form of SDCA that can handle general regularization term, which is of interest by itself.

stat.ML↗

arXiv2017

SAGA and Restricted Strong Convexity

SAGA is a fast incremental gradient method on the finite sum problem and its effectiveness has been tested on a vast of applications. In this paper, we analyze SAGA on a class of non-strongly convex and non-convex statistical problem such as Lasso, group Lasso, Logistic regression with $\ell_1$ regularization, linear regression with SCAD regularization and Correct Lasso. We prove that SAGA enjoys the linear convergence rate up to the statistical estimation accuracy, under the assumption of restricted strong convexity (RSC). It significantly extends the applicability of SAGA in convex and non-convex optimization.

stat.ML↗

arXiv2012

Dynamic Facial Expression of Emotion Made Easy

Facial emotion expression for virtual characters is used in a wide variety of areas. Often, the primary reason to use emotion expression is not to study emotion expression generation per se, but to use emotion expression in an application or research project. What is then needed is an easy to use and flexible, but also validated mechanism to do so. In this report we present such a mechanism. It enables developers to build virtual characters with dynamic affective facial expressions. The mechanism is based on Facial Action Coding. It is easy to implement, and code is available for download. To show the validity of the expressions generated with the mechanism we tested the recognition accuracy for 6 basic emotions (joy, anger, sadness, surprise, disgust, fear) and 4 blend emotions (enthusiastic, furious, frustrated, and evil). Additionally we investigated the effect of VC distance (z-coordinate), the effect of the VC's face morphology (male vs. female), the effect of a lateral versus a frontal presentation of the expression, and the effect of intensity of the expression. Participants (n=19, Western and Asian subjects) rated the intensity of each expression for each condition (within subject setup) in a non forced choice manner. All of the basic emotions were uniquely perceived as such. Further, the blends and confusion details of basic emotions are compatible with findings in psychology.

cs.HC↗