Bounds for Vector-Valued Function Estimation
This provides theoretical foundations for vector-valued learning problems, though it appears incremental in extending existing bounds to new contexts.
The authors developed a framework to derive risk bounds for vector-valued function estimation across various feature maps and loss functions, applying it to multi-task learning and multi-category learning as examples. They showed that conditions for beneficial shared representations in multi-task learning also apply to multi-category learning.
We present a framework to derive risk bounds for vector-valued learning with a broad class of feature maps and loss functions. Multi-task learning and one-vs-all multi-category learning are treated as examples. We discuss in detail vector-valued functions with one hidden layer, and demonstrate that the conditions under which shared representations are beneficial for multi- task learning are equally applicable to multi-category learning.