相关论文: Simplex Random Features

Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random…

In this paper we consider the problem of linear unmixing hidden random variables defined over the simplex with additive Gaussian noise, also known as probabilistic simplex component analysis (PRISM). Previous solutions to tackle this…

We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimisation problem, since the inflection point is unknown.…

Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…

Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…

This paper presents an enhanced adaptive random Fourier features (ARFF) training algorithm for shallow neural networks, building upon the work introduced in "Adaptive Random Fourier Features with Metropolis Sampling", Kammonen et al.,…

Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…

Neural Radiance Field (NeRF) technology has made significant strides in creating novel viewpoints. However, its effectiveness is hampered when working with sparsely available views, often leading to performance dips due to overfitting.…

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on applications in computational mechanics and design optimization. We leverage Mat\'ern-type…

Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of $k$ arguments is assumed to be continuous with…

We design the weights in consensus algorithms with spatially correlated random topologies. These arise with: 1) networks with spatially correlated random link failures and 2) networks with randomized averaging protocols. We show that the…

Random Feature Models (RFMs) have become a powerful tool for approximating multivariate functions and solving partial differential equations efficiently. Sparse Random Feature Expansions (SRFE) improve traditional RFMs by incorporating…

The method of random projection (RP) is the standard technique in machine learning and many other areas, for dimensionality reduction, approximate near neighbor search, compressed sensing, etc. Basically, RP provides a simple and effective…

In this technical report, we explore the behavior of Recursive Feature Machines (RFMs), a type of novel kernel machine that recursively learns features via the average gradient outer product, through a series of experiments on regression…

Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

Kernel method has been developed as one of the standard approaches for nonlinear learning, which however, does not scale to large data set due to its quadratic complexity in the number of samples. A number of kernel approximation methods…

We propose a random feature model for approximating high-dimensional sparse additive functions called the hard-ridge random feature expansion method (HARFE). This method utilizes a hard-thresholding pursuit-based algorithm applied to the…

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

We present a new framework for online Least Squares algorithms for nonlinear modeling in RKH spaces (RKHS). Instead of implicitly mapping the data to a RKHS (e.g., kernel trick), we map the data to a finite dimensional Euclidean space,…