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Approximating kernel functions with random features (RFs)has been a successful application of random projections for nonparametric estimation. However, performing random projections presents computational challenges for large-scale…
Kernel ridge regression is well-known to achieve minimax optimal rates in low-dimensional settings. However, its behavior in high dimensions is much less understood. Recent work establishes consistency for kernel regression under certain…
Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
Bayesian optimisation (BO) is a powerful framework for global optimisation of costly functions, using predictions from Gaussian process models (GPs). In this work, we apply BO to functions that exhibit invariance to a known group of…
While quantum annealing (QA) has been developed for combinatorial optimization, practical QA devices operate at finite temperature and under noise, and their outputs can be regarded as stochastic samples close to a Gibbs--Boltzmann…
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…
In Bayesian optimization (BO) for expensive black-box optimization tasks, acquisition function (AF) guides sequential sampling and plays a pivotal role for efficient convergence to better optima. Prevailing AFs usually rely on artificial…
Despite the recent deep learning (DL) revolution, kernel machines still remain powerful methods for action recognition. DL has brought the use of large datasets and this is typically a problem for kernel approaches, which are not scaling up…
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…
Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control. In this domain, kernel methods such as Gaussian process…
In machine learning, a critical class of decision-related problems concerns preventing predicted undesirable outcomes, referred to as the \textit{avoiding undesired future} (AUF) problem. To address this, the \textit{rehearsal learning}…
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…
This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…
Bayesian optimization (BO) is an efficient framework for optimizing expensive black-box functions. However, it is typically formulated as learning an end-to-end mapping from inputs to scalar objectives, thereby discarding the potentially…
The random feature (RF) approach is a well-established and efficient tool for scalable kernel methods, but existing literature has primarily focused on kernel ridge regression with random features (KRR-RF), which has limitations in handling…
Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…
Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and…
Traditional methods for black box optimization require a considerable number of evaluations which can be time consuming, unpractical, and often unfeasible for many engineering applications that rely on accurate representations and expensive…
Radial Basis Function Networks (RBFNs) are used primarily to solve curve-fitting problems and for non-linear system modeling. Several algorithms are known for the approximation of a non-linear curve from a sparse data set by means of RBFNs.…