Related papers: Structural interpretability in SVMs with truncated…
Support Vector Machine (SVM) is a state-of-the-art classification method widely used in science and engineering due to its high accuracy, its ability to deal with high dimensional data, and its flexibility in modeling diverse sources of…
This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite…
In the classical Gaussian SVM classification we use the feature space projection transforming points to normal distributions with fixed covariance matrices (identity in the standard RBF and the covariance of the whole dataset in Mahalanobis…
We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials, which provide an abstract formulation of quantum (q-) Fourier type systems. We prove Ismail conjecture…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…
Reproducing kernel Hilbert spaces (RKHSs) are key spaces for machine learning that are becoming popular also for linear system identification. In particular, the so-called stable RKHSs can be used to model absolutely summable impulse…
Motivation: The size of available omics datasets is steadily increasing with technological advancement in recent years. While this increase in sample size can be used to improve the performance of relevant prediction tasks in healthcare,…
Support Vector Machine (SVM) is a robust machine learning algorithm with broad applications in classification, regression, and outlier detection. SVM requires tuning the regularization parameter (RP) which controls the model capacity and…
In statistical learning, identifying underlying structures of true target functions based on observed data plays a crucial role to facilitate subsequent modeling and analysis. Unlike most of those existing methods that focus on some…
Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we…
While deep learning methods are increasingly being applied to tasks such as computer-aided diagnosis, these models are difficult to interpret, do not incorporate prior domain knowledge, and are often considered as a "black-box." The lack of…
The support vector machine (SVM) is a powerful and widely used classification algorithm. This paper uses the Karush-Kuhn-Tucker conditions to provide rigorous mathematical proof for new insights into the behavior of SVM. These insights…
In this work, we analyze the learnability of reproducing kernel Hilbert spaces (RKHS) under the $L^\infty$ norm, which is critical for understanding the performance of kernel methods and random feature models in safety- and…
Using the language of vertex operator algebras (VOAs) and vector-valued modular forms we study the modular group representations and spaces of 1-point functions associated to intertwining operators for Virasoro minimal model VOAs. We…
In this article, the reproducing kernel Hilbert space [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast…
Support Vector Machine (SVM) has been one of the most successful machine learning techniques for binary classification problems. The key idea is to maximize the margin from the data to the hyperplane subject to correct classification on…
Vision Transformer (ViT) architectures represent images as collections of high-dimensional vectorized tokens, each corresponding to a rectangular non-overlapping patch. This representation trades spatial granularity for embedding…
Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…
It is proven that encoding images and videos through Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, can lead to increased classification performance. Taking into account manifold…