Asymmetric kernels naturally exist in real life, e.g., for conditional probability and directed graphs. However, most of the existing kernel-based learning methods require kernels to be symmetric, which prevents the use of asymmetric kernels. This paper addresses the asymmetric kernel-based learning in the framework of the least squares support vector machine named AsK-LS, resulting in the first classification method that can utilize asymmetric kernels directly. We will show that AsK-LS can learn with asymmetric features, namely source and target features, while the kernel trick remains applicable, i.e., the source and target features exist but are not necessarily known. Besides, the computational burden of AsK-LS is as cheap as dealing with symmetric kernels. Experimental results on the Corel database, directed graphs, and the UCI database will show that in the case asymmetric information is crucial, the proposed AsK-LS can learn with asymmetric kernels and performs much better than the existing kernel methods that have to do symmetrization to accommodate asymmetric kernels.
Shanghai Jiao Tong University（上海交通大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
The random Fourier features (RFFs) method is a powerful and popular technique in kernel approximation for scalability of kernel methods. The theoretical foundation of RFFs is based on the Bochner theorem that relates symmetric, positive definite (PD) functions to probability measures. This condition naturally excludes asymmetric functions with a wide range applications in practice, e.g., directed graphs, conditional probability, and asymmetric kernels. Nevertheless, understanding asymmetric functions (kernels) and its scalability via RFFs is unclear both theoretically and empirically. In this …
Virginia Tech（弗吉尼亚理工大学）；Kuwait University（科威特大学）；Department of Industrial and Systems Engineering, Virginia Tech（弗吉尼亚理工大学工业与系统工程系）；Department of Industrial and Management Systems Engineering, Kuwait University（科威特大学工业与管理系统工程系）
Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive-to-evaluate. To tackle this challenge, Bayesian optimization, which conducts sequential design via a posterior distribution over the objective function, is a critical method used to find the global optimum of black-box functions. Kernel functions play an important role in shaping the posterior distribution of the estimated function. The widely used kernel function, e.g., radial basis function (RBF), is very vulnerable and susceptible to outliers; the existence of outliers is cau…
Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified to a linear inner product of the random Fourier features of those signals: random projections followed by a periodic map, the complex exponential. It is known that a simple quantization of those features (corresponding to replacing the complex exponential by a different periodic map that takes binary values, which is appealing for their transmission and stor…
Delft University of Technology（代尔夫特理工大学）；University of Amsterdam（阿姆斯特丹大学）
This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in the neighborhood of a certain sample through metric learning. We start by using data centers rather than all training samples. Subsequently, each center selects an individualized kernel metric. This enables each center to adjust the kernel space in its vicinity in correspondence with the topology of the targets --- a multi-modal approach. We additionally ad…
Beijing National Research Center for Information Science and Technology (BNRist)（北京信息科学与技术国家研究中心）；School of Software, Tsinghua University（清华大学软件学院）；Department of Automation, Tsinghua University（清华大学自动化系）；Institute for Brain and Cognitive Sciences, Tsinghua University（清华大学脑与认知科学研究所）；WMG Data Science, University of Warwick（华威大学WMG数据科学部）
As designing appropriate Convolutional Neural Network (CNN) architecture in the context of a given application usually involves heavy human works or numerous GPU hours, the research community is soliciting the architecture-neutral CNN structures, which can be easily plugged into multiple mature architectures to improve the performance on our real-world applications. We propose Asymmetric Convolution Block (ACB), an architecture-neutral structure as a CNN building block, which uses 1D asymmetric convolutions to strengthen the square convolution kernels. For an off-the-shelf architecture, we rep…
Xi’an Jiaotong University（西安交通大学）；Xi’an Microelectronic Technology Institute（西安微电子技术研究所）；Harbin Engineering University（哈尔滨工程大学）；National Space Science Center, Chinese Academy of Sciences（中国科学院国家空间科学中心）
In recent years, correntropy has been seccessfully applied to robust adaptive filtering to eliminate adverse effects of impulsive noises or outliers. Correntropy is generally defined as the expectation of a Gaussian kernel between two random variables. This definition is reasonable when the error between the two random variables is symmetrically distributed around zero. For the case of asymmetric error distribution, the symmetric Gaussian kernel is however inappropriate and cannot adapt to the error distribution well. To address this problem, in this brief we propose a new variant of correntro…
Variational Autoencoder Kernel Interpretation and Selection for Classification
University of Madeira（马德拉大学）；Interactive Technologies Institute（交互技术研究所）；Institute for Technological Development and Innovation in Communications, Universidad de Las Palmas de Gran Canaria（拉斯帕尔马斯大学通信技术发展与创新研究所）
College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics（南京航空航天大学计算机科学与技术学院）；Department of Radiology and BRIC, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校放射科与生物医学研究成像中心）
Recently, Nyström method has proved its prominence empirically and theoretically in speeding up the training of kernel machines while retaining satisfactory performances and accuracy. So far, there are several different approaches proposed to exploit Nyström method in scaling up kernel machines. However, there is no comparative study over these approaches, and they were individually analyzed for specific types of kernel machines. Therefore, it remains a question that the philosophy of which approach is more promising when it extends to other kernel machines. In this work, motivated by the colu…
Kernel PCA is a powerful feature extractor which recently has seen a reformulation in the context of Restricted Kernel Machines (RKMs). These RKMs allow for a representation of kernel PCA in terms of hidden and visible units similar to Restricted Boltzmann Machines. This connection has led to insights on how to use kernel PCA in a generative procedure, called generative kernel PCA. In this paper, the use of generative kernel PCA for exploring latent spaces of datasets is investigated. New points can be generated by gradually moving in the latent space, which allows for an interpretation of the…
University of Oxford（牛津大学）；Microsoft Research Cambridge（微软剑桥研究院）
Feature attribution for kernel methods is often heuristic and not individualised for each prediction. To address this, we turn to the concept of Shapley values~(SV), a coalition game theoretical framework that has previously been applied to different machine learning model interpretation tasks, such as linear models, tree ensembles and deep networks. By analysing SVs from a functional perspective, we propose \textsc{RKHS-SHAP}, an attribution method for kernel machines that can efficiently compute both \emph{Interventional} and \emph{Observational Shapley values} using kernel mean embeddings o…
Department of Informatics, Nicolaus Copernicus University（哥白尼大学信息学系）；is.umk.pl（哥白尼大学信息学系（注：此处为原机构网站，根据上下文应为哥白尼大学信息学系的一部分，严格按原文机构名提取））
Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite difficult, the use of a single kernel type may not be appropriate in all areas of the input space, convergence problems for some kernels are not uncommon, the standard quadratic programming solution has $O(m^3)$ time and $O(m^2)$ space complexity for $m$ training patterns. Kernel methods work because they implicitly provide new, useful features. Such features, deriv…
Building on the interpretation of a recurrent neural network (RNN) as a continuous-time neural differential equation, we show, under appropriate conditions, that the solution of a RNN can be viewed as a linear function of a specific feature set of the input sequence, known as the signature. This connection allows us to frame a RNN as a kernel method in a suitable reproducing kernel Hilbert space. As a consequence, we obtain theoretical guarantees on generalization and stability for a large class of recurrent networks. Our results are illustrated on simulated datasets.
