Related papers: Performance analysis of multi-dimensional ESPRIT-t…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
Regularized empirical risk minimization (rERM) has become important in data-intensive fields such as genomics and advertising, with stochastic gradient methods typically used to solve the largest problems. However, ill-conditioned…
We study direction-of-arrival (DOA) estimation from coarsely quantized data. We focus on a two-step approach which first estimates the signal subspace via covariance estimation and then extracts DOA angles by the ESPRIT algorithm. In…
We present a novel model designed for resource-efficient multichannel speech enhancement in the time domain, with a focus on low latency, lightweight, and low computational requirements. The proposed model incorporates explicit spatial and…
We introduce an interpretable deep learning approach for direction of arrival (DOA) estimation with a single snapshot. Classical subspace-based methods like MUSIC and ESPRIT use spatial smoothing on uniform linear arrays for single snapshot…
Two new stochastic variance-reduced algorithms named SARAH and SPIDER have been recently proposed, and SPIDER has been shown to achieve a near-optimal gradient oracle complexity for nonconvex optimization. However, the theoretical advantage…
Optimization-based samplers such as randomize-then-optimize (RTO) [2] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw…
In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically…
We investigate theoretically coherent detection implemented simultaneously on a set of mutually orthogonal spatial modes in the image plane as a method to characterize properties of a composite thermal source below the Rayleigh limit. A…
We revisit the classical problem of finding an approximately stationary point of the average of $n$ smooth and possibly nonconvex functions. The optimal complexity of stochastic first-order methods in terms of the number of gradient…
Large sample size brings the computation bottleneck for modern data analysis. Subsampling is one of efficient strategies to handle this problem. In previous studies, researchers make more fo- cus on subsampling with replacement (SSR) than…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
Online augmentation of an oblique aerial image sequence with structural information is an essential aspect in the process of 3D scene interpretation and analysis. One key aspect in this is the efficient dense image matching and depth…
We examine the optimal scaling and the efficiency of the pseudo-marginal random walk Metropolis algorithm using a recently-derived result on the limiting efficiency as the dimension, $d\rightarrow \infty$. We prove that the optimal scaling…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
Sparse depth measurements are widely available in many applications such as augmented reality, visual inertial odometry and robots equipped with low cost depth sensors. Although such sparse depth samples work well for certain applications…
We introduce SPIRAL, a SuPerlinearly convergent Incremental pRoximal ALgorithm, for solving nonconvex regularized finite sum problems under a relative smoothness assumption. Each iteration of SPIRAL consists of an inner and an outer loop.…
We propose a novel zeroth-order optimization algorithm based on an efficient sampling strategy. Under mild global regularity conditions on the objective function, we establish non-asymptotic convergence rates for the proposed method.…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to…