Related papers: A representer theorem for deep kernel learning

We propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our algorithm simultaneously computes support vectors and a proxy kernel matrix…

We consider the question of which nonconvex sets can be represented exactly as the feasible sets of mixed-integer convex optimization problems. We state the first complete characterization for the case when the number of possible integer…

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…

This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…

In this paper, we study the representation of neural networks from the view of kernels. We first define the Neural Fisher Kernel (NFK), which is the Fisher Kernel applied to neural networks. We show that NFK can be computed for both…

Despite the success of deep neural networks, there are still many challenges in deep representation learning due to the data scarcity issues such as data imbalance, unseen distribution, and domain shift. To address the above-mentioned…

This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

Learning the kernel functions used in kernel methods has been a vastly explored area in machine learning. It is now widely accepted that to obtain 'good' performance, learning a kernel function is the key challenge. In this work we focus on…

Many recurrent neural network machine learning paradigms can be formulated using state-space representations. The classical notion of canonical state-space realization is adapted in this paper to accommodate semi-infinite inputs so that it…

Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…

Representation learning is the foundation for the recent success of neural network models. However, the distributed representations generated by neural networks are far from ideal. Due to their highly entangled nature, they are di cult to…

In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals, including…

In this paper we investigate the connection between supervised learning and linear inverse problems. We first show that a linear inverse problem can be view as a function approximation problem in a reproducing kernel Hilbert space (RKHS)…

We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the…

We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called…

Deep learning has shown promising results in many machine learning applications. The hierarchical feature representation built by deep networks enable compact and precise encoding of the data. A kernel analysis of the trained deep networks…

We propose a general framework for policy representation for reinforcement learning tasks. This framework involves finding a low-dimensional embedding of the policy on a reproducing kernel Hilbert space (RKHS). The usage of RKHS based…

Neural models combining representation learning and reasoning in an end-to-end trainable manner are receiving increasing interest. However, their use is severely limited by their computational complexity, which renders them unusable on real…

One of the biggest challenges for deep learning algorithms in medical image analysis is the indiscriminate mixing of image properties, e.g. artifacts and anatomy. These entangled image properties lead to a semantically redundant feature…