On measure concentration of vector valued maps
نویسنده
چکیده
In this work, we study concentration properties for vector valued maps. In particular, we describe inequalities which capture the exact dimensional behavior of Lipschitz maps with values in Rk. To this task, we study in particular a domination principle for projections which might be of independent interest. We further compare our conclusions to earlier results by Pinelis in the Gaussian case, and discuss extensions to the infinite dimensional setting.
منابع مشابه
A new vector valued similarity measure for intuitionistic fuzzy sets based on OWA operators
Plenty of researches have been carried out, focusing on the measures of distance, similarity, and correlation between intuitionistic fuzzy sets (IFSs).However, most of them are single-valued measures and lack of potential for efficiency validation.In this paper, a new vector valued similarity measure for IFSs is proposed based on OWA operators.The vector is defined as a two-tuple consisting of ...
متن کاملHölder continuity of solution maps to a parametric weak vector equilibrium problem
In this paper, by using a new concept of strong convexity, we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric weak vector equilibrium problem in the case where the solution mapping is a general set-valued one. Without strong monotonicity assumptions, the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.
متن کاملOptimality conditions for Pareto efficiency and proper ideal point in set-valued nonsmooth vector optimization using contingent cone
In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.
متن کاملSHAPLEY FUNCTION BASED INTERVAL-VALUED INTUITIONISTIC FUZZY VIKOR TECHNIQUE FOR CORRELATIVE MULTI-CRITERIA DECISION MAKING PROBLEMS
Interval-valued intuitionistic fuzzy set (IVIFS) has developed to cope with the uncertainty of imprecise human thinking. In the present communication, new entropy and similarity measures for IVIFSs based on exponential function are presented and compared with the existing measures. Numerical results reveal that the proposed information measures attain the higher association with the existing me...
متن کاملOperator-Valued Bochner Theorem, Fourier Feature Maps for Operator-Valued Kernels, and Vector-Valued Learning
This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case. Our general setting is that of operator-valued kernels corresponding to RKHS of functions with values in a Hilbert space. We show that in general, for a give...
متن کامل