Related papers: Random Machines: A bagged-weighted support vector …
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…
We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework…
Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However,…
Improving the performance of classifiers is the realm of feature mapping, prototype selection, and kernel function transformations; these techniques aim for reducing the complexity, and also, improving the accuracy of models. In particular,…
Quantum kernels are considered as potential resources to illustrate benefits of quantum computing in machine learning. Considering the impact of hyperparameters on the performance of a classical machine learning model, it is imperative to…
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…
Thanks to their easy implementation via Radial Basis Functions (RBFs), meshfree kernel methods have been proved to be an effective tool for e.g. scattered data interpolation, PDE collocation, classification and regression tasks. Their…
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…
Model selection requires repeatedly evaluating models on a given dataset and measuring their relative performances. In modern applications of machine learning, the models being considered are increasingly more expensive to evaluate and the…
The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for…
Bias in datasets can be very detrimental for appropriate statistical estimation. In response to this problem, importance weighting methods have been developed to match any biased distribution to its corresponding target unbiased…
The computational complexity of kernel methods has often been a major barrier for applying them to large-scale learning problems. We argue that this barrier can be effectively overcome. In particular, we develop methods to scale up kernel…
Selecting important features in non-linear or kernel spaces is a difficult challenge in both classification and regression problems. When many of the features are irrelevant, kernel methods such as the support vector machine and kernel…
Kernel-based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods. Adopting the Bayesian perspective, the impulse response is modeled as a non-stationary Gaussian…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…
Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for…
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…