Related papers: Adaptive Random Fourier Features Training Stabiliz…
This work proposes a training algorithm based on adaptive random Fourier features (ARFF) with Metropolis sampling and resampling \cite{kammonen2024adaptiverandomfourierfeatures} for learning drift and diffusion components of stochastic…
The supervised learning problem to determine a neural network approximation $\mathbb{R}^d\ni x\mapsto\sum_{k=1}^K\hat\beta_k e^{{\mathrm{i}}\omega_k\cdot x}$ with one hidden layer is studied as a random Fourier features algorithm. The…
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…
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…
A major challenge to out-of-distribution generalization is reliance on spurious features -- patterns that are predictive of the class label in the training data distribution, but not causally related to the target. Standard methods for…
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…
The overfitting is one of the cursing subjects in the deep learning field. To solve this challenge, many approaches were proposed to regularize the learning models. They add some hyper-parameters to the model to extend the generalization;…
Random Fourier Features (RFF) is among the most popular and broadly applicable approaches for scaling up kernel methods. In essence, RFF allows the user to avoid costly computations on a large kernel matrix via a fast randomized…
We propose the adaptive random Fourier features Gaussian kernel LMS (ARFF-GKLMS). Like most kernel adaptive filters based on stochastic gradient descent, this algorithm uses a preset number of random Fourier features to save computation…
Typical person re-identification (re-ID) methods train a deep CNN to extract deep features and combine them with a distance metric for the final evaluation. In this work, we focus on exploiting the full information encoded in the deep…
This paper introduces the Asymptotic-Preserving Random Feature Method (APRFM) for the efficient resolution of multiscale radiative transfer equations. The APRFM effectively addresses the challenges posed by stiffness and multiscale…
Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…
We present experimental results highlighting two key differences resulting from the choice of training algorithm for two-layer neural networks. The spectral bias of neural networks is well known, while the spectral bias dependence on the…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…
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…
In this paper, a novel and robust algorithm is proposed for adaptive beamforming based on the idea of reconstructing the autocorrelation sequence (ACS) of a random process from a set of measured data. This is obtained from the first column…
Feature compression is increasingly important for improving the efficiency of downstream tasks, especially in applications involving large-scale or multi-modal data. While existing methods typically rely on dedicated models for achieving…
Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…
This article characterizes the exact asymptotics of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples $n$, their dimension $p$, and the dimension of feature space $N$ are all large and…
We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared to a set of benchmark methods including…