Related papers: Random Fourier Signature Features
Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…
The signature kernel is a kernel between time series of arbitrary length and comes with strong theoretical guarantees from stochastic analysis. It has found applications in machine learning such as covariance functions for Gaussian…
The signature kernel is a positive definite kernel for sequential data. It inherits theoretical guarantees from stochastic analysis, has efficient algorithms for computation, and shows strong empirical performance. In this short survey…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…
The signature kernel is a recent state-of-the-art tool for analyzing high-dimensional sequential data, valued for its theoretical guarantees and strong empirical performance. In this paper, we present a novel method for efficiently…
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…
Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…
In this paper, we propose a fast surrogate leverage weighted sampling strategy to generate refined random Fourier features for kernel approximation. Compared to the current state-of-the-art method that uses the leverage weighted scheme…
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…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…
Kernel methods have recently attracted resurgent interest, showing performance competitive with deep neural networks in tasks such as speech recognition. The random Fourier features map is a technique commonly used to scale up kernel…
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…
Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…
Simulation models of complex dynamics in the natural and social sciences commonly lack a tractable likelihood function, rendering traditional likelihood-based statistical inference impossible. Recent advances in machine learning have…
Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…