Learning Vector Valued Functions : Beyond Tikhonov RegularizationBaldassarre, LucaBarla, AnnalisaRosasco, LorenzoVerri, Alessandro
本文继续介绍 MATHEMATICS FOR MACHINE LEARNING[1]第五章向量微积分[2]部分的内容。这部分例题较多,可以结合相关例子深入理解相关概念、定义。机器学习中的许多算法是根据一组期望的模型参数来优化目标函数的,…
Derivatives of Vector-Valued FunctionsLearning OutcomesWrite an expression for the derivative of a vector-valued function Now that we have seen what a vector-valued function is and how to take its limit, the next step is to learn how to differentiate a vector-valued function. The definition of...
the vector obtained by calculating the definite integral of each of the component functions of a given vector-valued function, then using the results as the components of the resulting function derivative of a vector-valued function the derivative of a vector-valued functionr(t)r(t)isr′(t)=...
About this book series The series in Vector Optimization contains publications in various fields of optimization with vector-valued objective functions, such as multiobjective optimization, multi criteria decision making, set optimization, vector-valued game theory and border areas to financial mathematics,...
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It has been observed that the theory of vector valued reproducing kernel Hilbert spaces associated with operator valued kernel functions arises naturally in many areas like probability and stochastic process, machine learning, statistics, etc., and is an active area of research. For example, the ...
In Section 5, we investigate regularized learning schemes in vector-valued RKBSs. 2. Definition and basic properties We are concerned with spaces of functions from a fixed set to a vector space. We shall allow the space of functions and the range space both to be a Banach space. Our key...
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Vector-valued analytic functions in C n , which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space H p , 1 ≤ p < 2 , if the boundary value is in the vector-valued L p , 1 ≤ p < 2 , functions. The analysis of this pap...