Related papers: Kernel-based dequantization of variational QML wit…
Kernel methods provide a flexible and theoretically grounded approach to nonlinear and nonparametric learning. While memory and run-time requirements hinder their applicability to large datasets, many low-rank kernel approximations, such as…
In this work, we introduce kernels with random Fourier features in the meta-learning framework to leverage their strong few-shot learning ability. We propose meta variational random features (MetaVRF) to learn adaptive kernels for the…
The emergence of Quantum Machine Learning (QML) to enhance traditional classical learning methods has seen various limitations to its realisation. There is therefore an imperative to develop quantum models with unique model hypotheses to…
The method of "random Fourier features (RFF)" has become a popular tool for approximating the "radial basis function (RBF)" kernel. The variance of RFF is actually large. Interestingly, the variance can be substantially reduced by a simple…
The method of random projection (RP) is the standard technique in machine learning and many other areas, for dimensionality reduction, approximate near neighbor search, compressed sensing, etc. Basically, RP provides a simple and effective…
Kernel methods form a powerful, versatile, and theoretically-grounded unifying framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the kernel trick to perform pairwise evaluations…
In recent years, parameterized quantum circuits have been regarded as machine learning models within the framework of the hybrid quantum-classical approach. Quantum machine learning (QML) has been applied to binary classification problems…
Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this Review, we provide a structured overview of recent advances that bridge foundational…
We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of $1$-bit…
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…
Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…
Kernel power $k$-means (KPKM) leverages a family of means to mitigate local minima issues in kernel $k$-means. However, KPKM faces two key limitations: (1) the computational burden of the full kernel matrix restricts its use on extensive…
We investigate how to train kernel approximation methods that generalize well under a memory budget. Building on recent theoretical work, we define a measure of kernel approximation error which we find to be more predictive of the empirical…
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…
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…
Quantum machine learning (QML) is the use of quantum computing for the computation of machine learning algorithms. With the prevalence and importance of classical data, a hybrid quantum-classical approach to QML is called for. Parameterized…
Radial basis function (RBF) networks are expanded to incorporate quantum kernel functions enabling a new type of hybrid quantum-classical machine learning algorithm. Using this approach, synthetic examples are introduced which allow for…
Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…
We propose a Gradient Boosting algorithm for learning an ensemble of kernel functions adapted to the task at hand. Unlike state-of-the-art Multiple Kernel Learning techniques that make use of a pre-computed dictionary of kernel functions to…
This paper introduces a novel approach for multi-task regression that connects Kernel Machines (KMs) and Extreme Learning Machines (ELMs) through the exploitation of the Random Fourier Features (RFFs) approximation of the RBF kernel. In…