Universal Kernels for Multi-Task Learning
نویسندگان
چکیده
In this paper we are concerned with reproducing kernel Hilbert spaces HK of functions from an input space into a Hilbert space Y, an environment appropriate for multi-task learning. The reproducing kernel K associated to HK has its values as operators on Y. Our primary goal here is to derive conditions which ensure that the kernel K is universal. This means that on every compact subset of the input space, every continuous function with values in Y can be uniformly approximated by sections of the kernel. We provide various characterizations of universal kernels and highlight them with several concrete examples of some practical importance. Our analysis uses basic principles of functional analysis and especially the useful notion of vector measures which we describe in sufficient detail to clarify our results.
منابع مشابه
Universal Multi-Task Kernels
In this paper we are concerned with reproducing kernel Hilbert spaces HK of functions from an input space into a Hilbert space Y , an environment appropriate for multi-task learning. The reproducing kernel K associated to HK has its values as operators on Y . Our primary goal here is to derive conditions which ensure that the kernel K is universal. This means that on every compact subset of the...
متن کاملStability of Multi-Task Kernel Regression Algorithms
We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning problems with nonscalar outputs like multi-task learning and structured output prediction. We show that multi-task kernel regression algorithms are uniformly stable in the general case of infinite-d...
متن کاملMulti-task and Lifelong Learning of Kernels
We consider a problem of learning kernels for use in SVM classification in the multi-task and lifelong scenarios and provide generalization bounds on the error of a large margin classifier. Our results show that, under mild conditions on the family of kernels used for learning, solving several related tasks simultaneously is beneficial over single task learning. In particular, as the number of ...
متن کاملKernels for Multi--task Learning
This paper provides a foundation for multi–task learning using reproducing kernel Hilbert spaces of vector–valued functions. In this setting, the kernel is a matrix–valued function. Some explicit examples will be described which go beyond our earlier results in [7]. In particular, we characterize classes of matrix– valued kernels which are linear and are of the dot product or the translation in...
متن کاملMulti-Task Learning Using Neighborhood Kernels
This paper introduces a new and effective algorithm for learning kernels in a Multi-Task Learning (MTL) setting. Although, we consider a MTL scenario here, our approach can be easily applied to standard single task learning, as well. As shown by our empirical results, our algorithm consistently outperforms the traditional kernel learning algorithms such as uniform combination solution, convex c...
متن کامل