Vector-Valued RKHS
A vector-valued reproducing kernel Hilbert space is a reproducing kernel Hilbert space whose values lie in a vector space, with a kernel function that returns an operator (matrix) rather than a scalar. It can simultaneously encode similarities between input samples and correlations among the components of output vectors, and is widely used in multi-task learning and structured output regression.
Timeline (last 90 days)
The paper uniformly models hierarchical forecasting as a multivariate regression problem in a vector-valued reproducing kernel Hilbert space, embedding the consistency constraint into the hypothesis space through a structured operator-valued kernel.
Functions in a vector-valued RKHS take values in R^d, and their kernel function K(x,x') returns a d×d matrix (operator), encoding not only sample similarity but also the correlations among output components.
All Facts (2)
The paper uniformly models hierarchical forecasting as a multivariate regression problem in a vector-valued reproducing kernel Hilbert space, embedding the consistency constraint into the hypothesis space through a structured operator-valued kernel.
50%UnverifiedFunctions in a vector-valued RKHS take values in R^d, and their kernel function K(x,x') returns a d×d matrix (operator), encoding not only sample similarity but also the correlations among output components.
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