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)=...
Motivated by our theoretical analysis, we propose a general semi-supervised algorithm for efficiently learning vector-valued functions, incorporating both local Rademacher complexity and Laplacian regularization. Extensive experimental results illustrate the proposed algorithm significantly outperforms the compared ...
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A real-valued function F(x) may be defined in a vector form as follows: (1.10)F(x)=[F1,F2,…,Fm],F:Rn→Rm where Fi, i = 1,…,m the elements of the matrix F are real-valued functions of real numbers. If F(x) is a scalar matrix, its gradient is defined as follows: ...
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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,...
We deal with the minimax problem relative to a vector-valued functionf: X 0×Y 0 V, where a partial ordering in the topological vector spaceV is induced by a closed and convex coneC. In Ref. 1, under suitable hypotheses, we proved that $$Max\bigcup\limits_{s\varepsilon X_0 } {Mi...