Related papers: Orthogonal Random Features
We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn…
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…
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,…
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…
We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the…
This paper presents a simple and efficient method to convolve an image with a Gaussian kernel. The computation is performed in a constant number of operations per pixel using running sums along the image rows and columns. We investigate the…
Feature selection for predictive analytics is the problem of identifying a minimal-size subset of features that is maximally predictive of an outcome of interest. To apply to molecular data, feature selection algorithms need to be scalable…
We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…
Random non-linear Fourier features have recently shown remarkable performance in a wide-range of regression and classification applications. Motivated by this success, this article focuses on a sparse non-linear Fourier feature (NFF) model.…
Recently, randomized algorithms for low-rank approximation of quaternion matrices have received increasing attention. However, for large-scale problems, existing quaternion orthonormalizations are inefficient, leading to slow rangefinders.…
An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…
Randomized algorithms for low-rank matrix approximation are investigated, with the emphasis on the fixed-precision problem and computational efficiency for handling large matrices. The algorithms are based on the so-called QB factorization,…
The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations. Graph Signal Processing (GSP) is a recent…
We analyze a sublinear RAlSFA (Randomized Algorithm for Sparse Fourier Analysis) that finds a near-optimal B-term Sparse Representation R for a given discrete signal S of length N, in time and space poly(B,log(N)), following the approach…
Orthogonal time frequency space (OTFS) modulation was proposed to tackle the destructive Doppler effects in wireless communications, with potential applications to many other areas. In this paper, we investigate its application to radar…
Sparse Filtering is a popular feature learning algorithm for image classification pipelines. In this paper, we connect the performance of Sparse Filtering with spectral properties of the corresponding feature matrices. This connection…
We study the theoretical properties of random Fourier features classification with Lipschitz continuous loss functions such as support vector machine and logistic regression. Utilizing the regularity condition, we show for the first time…
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…
In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…