Related papers: Generalized Reference Kernel for One-class Classif…
Kernel Regularized Least Squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing…
Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…
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,…
We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student…
Analysis of large-scale sequential data has been one of the most crucial tasks in areas such as bioinformatics, text, and audio mining. Existing string kernels, however, either (i) rely on local features of short substructures in the…
As quantum computers become increasingly practical, so does the prospect of using quantum computation to improve upon traditional algorithms. Kernel methods in machine learning is one area where such improvements could be realized in the…
We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…
Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…
Training Deep Convolutional Neural Networks (CNNs) is based on the notion of using multiple kernels and non-linearities in their subsequent activations to extract useful features. The kernels are used as general feature extractors without…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
In this article a surprising result is demonstrated using the neural tangent kernel. This kernel is defined as the inner product of the vector of the gradient of an underlying model evaluated at training points. This kernel is used to…
Boosting combines weak (biased) learners to obtain effective learning algorithms for classification and prediction. In this paper, we show a connection between boosting and kernel-based methods, highlighting both theoretical and practical…
A random forest is a popular tool for estimating probabilities in machine learning classification tasks. However, the means by which this is accomplished is unprincipled: one simply counts the fraction of trees in a forest that vote for a…
Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on…
We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…
We propose a general class of sample based explanations of machine learning models, which we term generalized representers. To measure the effect of a training sample on a model's test prediction, generalized representers use two…
Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are…
Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large…