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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…
Support Vector Machines (SVMs) are powerful learners that have led to state-of-the-art results in various computer vision problems. SVMs suffer from various drawbacks in terms of selecting the right kernel, which depends on the image…
The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…
Deep kernel map networks have shown excellent performances in various classification problems including image annotation. Their general recipe consists in aggregating several layers of singular value decompositions (SVDs) -- that map data…
Kernel methods are a highly effective and widely used collection of modern machine learning algorithms. A fundamental limitation of virtually all such methods are computations involving the kernel matrix that naively scale quadratically…
The Gaussian kernel is a very popular kernel function used in many machine learning algorithms, especially in support vector machines (SVMs). It is more often used than polynomial kernels when learning from nonlinear datasets, and is…
For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…
Kernel-based machine learning algorithms are based on mapping data from the original input feature space to a kernel feature space of higher dimensionality to solve a linear problem in that space. Over the last decade, kernel based…
Stein variational gradient descent (SVGD) and its variants have shown promising successes in approximate inference for complex distributions. In practice, we notice that the kernel used in SVGD-based methods has a decisive effect on the…
Support vector machines (SVM) and other kernel techniques represent a family of powerful statistical classification methods with high accuracy and broad applicability. Because they use all or a significant portion of the training data,…
This paper examines the application of a Quantum Support Vector Machine (QSVM) for radarbased aerial target classification using micro-Doppler signatures. Classical features are extracted and reduced via Principal Component Analysis (PCA)…
In the last few years, various types of machine learning algorithms, such as Support Vector Machine (SVM), Support Vector Regression (SVR), and Non-negative Matrix Factorization (NMF) have been introduced. The kernel approach is an…
The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation…
We show that a deep neural network (DNN) trained to construct a stochastic discount factor (SDF) admits a sharp additive decomposition that separates nonlinear characteristic discovery from the pricing rule that aggregates them. The…
A vast amount of literature has recently focused on the "Neural Collapse" (NC) phenomenon, which emerges when training neural network (NN) classifiers beyond the zero training error point. The core component of NC is the decrease in the…
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…
One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…
Quantum Support Vector Machine is a kernel-based approach to classification problems. We study the applicability of quantum kernels to financial data, specifically our self-curated Dhaka Stock Exchange (DSEx) Broad Index dataset. To the…
We introduce kernel density machines (KDM), an agnostic kernel-based framework for learning the Radon-Nikodym derivative (density) between probability measures under minimal assumptions. KDM applies to general measurable spaces and avoids…
Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by…