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Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…

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…

Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…

To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…

Kernel learning methods are among the most effective learning methods and have been vigorously studied in the past decades. However, when tackling with complicated tasks, classical kernel methods are not flexible or "rich" enough to…

Estimating a covariance matrix is an important task in applications where the number of variables is larger than the number of observations. Shrinkage approaches for estimating a high-dimensional covariance matrix are often employed to…

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…

Recovering a low-rank signal matrix from its noisy observation, commonly known as matrix denoising, is a fundamental inverse problem in statistical signal processing. Matrix denoising methods are generally based on shrinkage or thresholding…

Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to…

This paper proposes a novel graph-based regularized regression estimator - the hierarchical feature regression (HFR) -, which mobilizes insights from the domains of machine learning and graph theory to estimate robust parameters for a…

Linear model prediction with a large number of potential predictors is both statistically and computationally challenging. The traditional approaches are largely based on shrinkage selection/estimation methods, which are applicable even…

Kernel mean embedding is a useful tool to represent and compare probability measures. Despite its usefulness, kernel mean embedding considers infinite-dimensional features, which are challenging to handle in the context of differentially…

Kernel methods have recently attracted resurgent interest, showing performance competitive with deep neural networks in tasks such as speech recognition. The random Fourier features map is a technique commonly used to scale up kernel…

Random forest regression is a powerful non-parametric method that adapts to local data characteristics through data-driven partitioning, making it effective across diverse application domains. However, the piecewise constant nature of…

Many applications of quantum computing in the near term rely on variational quantum circuits (VQCs). They have been showcased as a promising model for reaching a quantum advantage in machine learning with current noisy intermediate scale…

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…

Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…

Stein's paradox holds considerable sway in high-dimensional statistics, highlighting that the sample mean, traditionally considered the de facto estimator, might not be the most efficacious in higher dimensions. To address this, the…

A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…

Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…