相关论文: Theoretical and Experimental Analysis of a Randomi…

We study the algorithmic problem of sparse mean estimation in the presence of adversarial outliers. Specifically, the algorithm observes a \emph{corrupted} set of samples from $\mathcal{N}(\mu,\mathbf{I}_d)$, where the unknown mean $\mu \in…

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…

Fourier transformations of pseudo-Boolean functions are popular tools for analyzing functions of binary sequences. Real-world functions often have structures that manifest in a sparse Fourier transform, and previous works have shown that…

In this paper, we derive a new reconstruction method for real non-harmonic Fourier sums, i.e., real signals which can be represented as sparse exponential sums of the form $f(t) = \sum_{j=1}^{K} \gamma_{j} \, \cos(2\pi a_{j} t + b_{j})$,…

In recent years, a number of works have studied methods for computing the Fourier transform in sublinear time if the output is sparse. Most of these have focused on the discrete setting, even though in many applications the input signal is…

Computing Fourier transforms of k-sparse signals, where only k of N frequencies are non-zero, is fundamental in compressed sensing, radar, and medical imaging. While the Fast Fourier Transform (FFT) evaluates all N frequencies in $O(N \log…

We consider the problem of computing the Walsh-Hadamard Transform (WHT) of some $N$-length input vector in the presence of noise, where the $N$-point Walsh spectrum is $K$-sparse with $K = {O}(N^{\delta})$ scaling sub-linearly in the input…

Relative impulse responses between microphones are usually long and dense due to the reverberant acoustic environment. Estimating them from short and noisy recordings poses a long-standing challenge of audio signal processing. In this paper…

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.,…

In this paper we consider the special case where a discrete signal ${\bf x}$ of length N is known to vanish outside a support interval of length $m < N$. If the support length $m$ of ${\bf x}$ or a good bound of it is a-priori known we…

Decomposing a flow on a Directed Acyclic Graph (DAG) into a weighted sum of a small number of paths is an essential task in operations research and bioinformatics. This problem, referred to as Sparse Flow Decomposition (SFD), has gained…

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…

Nonstationary signals are commonly analyzed and processed in the time-frequency (T-F) domain that is obtained by the discrete Gabor transform (DGT). The T-F representation obtained by DGT is spread due to windowing, which may degrade the…

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,…

Time-frequency (TF) representation of non-stationary signals typically requires the effective concentration of energy distribution along the instantaneous frequency (IF) ridge, which exhibits intrinsic sparsity. Inspired by the sparse…

Given a multiset $S$ of $n$ positive integers and a target integer $t$, the Subset Sum problem asks to determine whether there exists a subset of $S$ that sums up to $t$. The current best deterministic algorithm, by Koiliaris and Xu…

Nonlinear sparse sensing (NSS) techniques have been adopted for realizing compressive sensing (CS) in many applications such as Radar imaging and sparse channel estimation. Unlike the NSS, in this paper, we propose an adaptive sparse…

Machine learning and artificial intelligence algorithms typically require large amount of data for training. This means that for nonlinear aeroelastic applications, where small training budgets are driven by the high computational burden…

Computing the Fourier transform of a $q$-ary function $f:\mathbb{Z}_{q}^n\rightarrow \mathbb{R}$, which maps $q$-ary sequences to real numbers, is an important problem in mathematics with wide-ranging applications in biology, signal…

We design a new distribution over $\poly(r \eps^{-1}) \times n$ matrices $S$ so that for any fixed $n \times d$ matrix $A$ of rank $r$, with probability at least 9/10, $\norm{SAx}_2 = (1 \pm \eps)\norm{Ax}_2$ simultaneously for all $x \in…