Representer Theorems for Metric and Preference Learning: A Geometric Perspective
We explore the metric and preference learning problem in Hilbert spaces. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key observation is that the representer theorem can be formulated with respect to the norm induced by the inner product inherent in the problem structure. Additionally, we demonstrate how our framework can be applied to the task of metric learning from triplet comparisons and show that it leads to a simple and self-contained representer theorem for this task. In the case of Reproducing Kernel Hilbert Spaces (RKHS), we demonstrate that the solution to the learning problem can be expressed using kernel terms, akin to classical representer theorems.
Code (0)
등록된 구현이 없습니다.
Tasks
Metric LearningTripletSimilar Papers 제목 키워드 기반
Approximate Representer Theorems in Non-reflexive Banach Spaces
The representer theorem is one of the most important mathematical foundations for regularised learning and kernel methods. Classical formulations of the theorem state sufficient conditions under which a regularisation pr…
When is there a Representer Theorem? Reflexive Banach spaces
We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the l…
Learning TheoryFeatured Reproducing Kernel Banach Spaces for Learning and Neural Networks
Reproducing kernel Hilbert spaces provide a foundational framework for kernel-based learning, where regularization and interpolation problems admit finite-dimensional solutions through classical representer theorems. Man…
Non-Parametric Representation Learning with Kernels
Unsupervised and self-supervised representation learning has become popular in recent years for learning useful features from unlabelled data. Representation learning has been mostly developed in the neural network liter…
Representation LearningSelf-Supervised LearningSparse Representer Theorems for Learning in Reproducing Kernel Banach Spaces
Sparsity of a learning solution is a desirable feature in machine learning. Certain reproducing kernel Banach spaces (RKBSs) are appropriate hypothesis spaces for sparse learning methods. The goal of this paper is to und…
Sparse Learning