Exact Controllability of Linear Stochastic Differential Equations and Related Problems

A notion of $L^p$-exact controllability is introduced for linear controlled (forward) stochastic differential equations, for which several sufficient conditions are established. Further, it is proved that the $L^p$-exact controllability, the validity of an observability inequality for the adjoint equation, the solvability of an optimization problem, and the solvability of an $L^p$-type norm optimal control problem are all equivalent

From Common to Special: When Multi-Attribute Learning Meets Personalized Opinions

Visual attributes, which refer to human-labeled semantic annotations, have gained increasing popularity in a wide range of real world applications. Generally, the existing attribute learning methods fall into two categories: one focuses on learning user-specific labels separately for different attributes, while the other one focuses on learning crowd-sourced global labels jointly for multiple attributes. However, both categories ignore the joint effect of the two mentioned factors: the personal diversity with respect to the global consensus; and the intrinsic correlation among multiple attributes. To overcome this challenge, we propose a novel model to learn user-specific predictors across multiple attributes. In our proposed model, the diversity of personalized opinions and the intrinsic relationship among multiple attributes are unified in a common-to-special manner. To this end, we adopt a three-component decomposition. Specifically, our model integrates a common cognition factor, an attribute-specific bias factor and a user-specific bias factor. Meanwhile Lasso and group Lasso penalties are adopted to leverage efficient feature selection. Furthermore, theoretical analysis is conducted to show that our proposed method could reach reasonable performance. Eventually, the empirical study carried out in this paper demonstrates the effectiveness of our proposed method