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The use of episodic memory in continual learning has demonstrated effectiveness for alleviating catastrophic forgetting. In recent studies, gradient-based approaches have been developed to make more efficient use of compact episodic memory.…
Pairwise learning or dyadic prediction concerns the prediction of properties for pairs of objects. It can be seen as an umbrella covering various machine learning problems such as matrix completion, collaborative filtering, multi-task…
This paper addresses the scalability problem of Bayesian deep neural networks. The performance of deep neural networks is undermined by the fact that these algorithms have poorly calibrated measures of uncertainty. This restricts their…
The paper introduces a new efficient nonlinear one-class classifier formulated as the Rayleigh quotient criterion optimisation. The method, operating in a reproducing kernel Hilbert space, minimises the scatter of target distribution along…
Physics-informed machine learning (PIML) has emerged as a promising alternative to conventional numerical methods for solving partial differential equations (PDEs). PIML models are increasingly built via deep neural networks (NNs) whose…
Feature attribution for kernel methods is often heuristic and not individualised for each prediction. To address this, we turn to the concept of Shapley values~(SV), a coalition game theoretical framework that has previously been applied to…
Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…
We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous, and incremental response curves. Treatment and covariates may be discrete or continuous in general spaces. Due to a…
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…
Kernel methods play a critical role in many machine learning algorithms. They are useful in manifold learning, classification, clustering and other data analysis tasks. Setting the kernel's scale parameter, also referred to as the kernel's…
Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In \emph{Kernelized Diffusion Maps} (KDM), the kernel determines the accuracy of the RKHS estimator of a diffusion-type operator and hence the quality…
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…
While the depth of modern Convolutional Neural Networks (CNNs) surpasses that of the pioneering networks with a significant margin, the traditional way of appending supervision only over the final classifier and progressively propagating…
In recent years, large amounts of electronic health records (EHRs) concerning chronic diseases have been collected to facilitate medical diagnosis. Modeling the dynamic properties of EHRs related to chronic diseases can be efficiently done…
Self-supervised learning (SSL) has emerged as a powerful strategy for representation learning under limited annotation regimes, yet its effectiveness remains highly sensitive to many factors, especially the nature of the target task. In…
A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical priors, typically encoded through the PDE operator, into a…
Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore…
Kernel-based statistical methods are efficient, but their performance depends heavily on the selection of kernel parameters. In literature, the optimization studies on kernel-based chemometric methods is limited and often reduced to grid…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
Existing approaches often enhance the performance of single-image super-resolution (SISR) methods by incorporating auxiliary structures, such as specialized loss functions, to indirectly boost the quality of low-resolution images. In this…