Related papers: Quiver Laplacians and Feature Selection
We study QPT (quasi-polynomial tractability) in the worst case setting for linear tensor product problems defined over Hilbert spaces. We assume that the domain space is a reproducing kernel Hilbert space so that function values are well…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
The problem of selecting an appropriate number of features in supervised learning problems is investigated in this paper. Starting with common methods in machine learning, we treat the feature selection task as a quadratic unconstrained…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Kernel-based feature selection is an important tool in nonparametric statistics. Despite many practical applications of kernel-based feature selection, there is little statistical theory available to support the method. A core challenge is…
As deep vision models' popularity rapidly increases, there is a growing emphasis on explanations for model predictions. The inherently explainable attribution method aims to enhance the understanding of model behavior by identifying the…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
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…
This paper introduces a novel methodology for Feature Selection for Functional Classification, FSFC, that addresses the challenge of jointly performing feature selection and classification of functional data in scenarios with categorical…
A central problem in machine learning and pattern recognition is the process of recognizing the most important features. In this paper, we provide a new feature selection method (DRPT) that consists of first removing the irrelevant features…
Quasi-Helmholtz decompositions are fundamental tools in integral equation modeling of electromagnetic problems because of their ability of rescaling solenoidal and non-solenoidal components of solutions, operator matrices, and radiated…
Many problems in machine learning can be expressed by means of a graph with nodes representing training samples and edges representing the relationship between samples in terms of similarity, temporal proximity, or label information. Graphs…
Vision Transformer (ViT) models have demonstrated a breakthrough in a wide range of computer vision tasks. However, compared to the Convolutional Neural Network (CNN) models, it has been observed that the ViT models struggle to capture…
In this paper, we present a new adaptive feature scaling scheme for ultrahigh-dimensional feature selection on Big Data. To solve this problem effectively, we first reformulate it as a convex semi-infinite programming (SIP) problem and then…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…
In this paper, we cast the scribble-based interactive image segmentation as a semi-supervised learning problem. Our novel approach alleviates the need to solve an expensive generalized eigenvector problem by approximating the eigenvectors…
Dimensionality reduction is the fundamental problem for machine learning and pattern recognition. During data preprocessing, the feature selection is often demanded to reduce the computational complexity. The problem of feature selection is…
Dynamic inner principal component analysis (DiPCA) is a powerful method for the analysis of time-dependent multivariate data. DiPCA extracts dynamic latent variables that capture the most dominant temporal trends by solving a large-scale,…
Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as…