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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…
In the quest for quantum advantage, a central question is under what conditions can classical algorithms achieve a performance comparable to quantum algorithms--a concept known as dequantization. Random Fourier features (RFFs) have…
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…
Developing efficient kernel methods for regression is very popular in the past decade. In this paper, utilizing boosting on kernel-based weaker learners, we propose a novel kernel-based learning algorithm called kernel-based re-scaled…
Slow kinetic processes of molecular systems can be analyzed by computing dominant eigenpairs of the Koopman operator or its generator. In this context, the Variational Approach to Markov Processes (VAMP) provides a rigorous way of…
Linearization of attention using various kernel approximation and kernel learning techniques has shown promise. Past methods used a subset of combinations of component functions and weight matrices within the random feature paradigm. We…
We propose a new method for feature learning and function estimation in supervised learning via regularised empirical risk minimisation. Our approach considers functions as expectations of Sobolev functions over all possible one-dimensional…
In large-scale regression problems, random Fourier features (RFFs) have significantly enhanced the computational scalability and flexibility of Gaussian processes (GPs) by defining kernels through their spectral density, from which a finite…
Kernel function plays a crucial role in machine learning algorithms such as classifiers. In this paper, we aim to improve the classification performance and reduce the reading out burden of quantum classifiers. We devise a universally…
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…
The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we…
This paper introduces kernel continual learning, a simple but effective variant of continual learning that leverages the non-parametric nature of kernel methods to tackle catastrophic forgetting. We deploy an episodic memory unit that…
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 present a probabilistic framework for both (i) determining the initial settings of kernel adaptive filters (KAFs) and (ii) constructing fully-adaptive KAFs whereby in addition to weights and dictionaries, kernel parameters are learnt…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
Typical machine learning approaches require centralized data for model training, which may not be possible where restrictions on data sharing are in place due to, for instance, privacy and gradient protection. The recently proposed…
This paper presents a novel technique based on gradient boosting to train the final layers of a neural network (NN). Gradient boosting is an additive expansion algorithm in which a series of models are trained sequentially to approximate a…
Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample…
Classification is a common task in machine learning. Random features (RFs) stand as a central technique for scalable learning algorithms based on kernel methods, and more recently proposed optimized random features, sampled depending on the…
Deep convolutional neural networks have achieved remarkable success in face recognition (FR), partly due to the abundant data availability. However, the current training benchmarks exhibit an imbalanced quality distribution; most images are…