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Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…
Out-of-Distribution (OoD) detection is important for building safe artificial intelligence systems. However, current OoD detection methods still cannot meet the performance requirements for practical deployment. In this paper, we propose a…
Advances in deep learning have enabled physics-informed neural networks to solve partial differential equations. Numerical differentiation using the finite-difference (FD) method is efficient in physics-constrained designs, even in…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…
Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems. In testing data quality, for example, one may study the distance of a given dataset, viewed as a…
In this paper, we develop a new technique to obtain nearly optimal estimates of the computational resolution limits introduced in Appl. Comput. Harmon. Anal. 56 (2022) 402-446; IEEE Trans. Inf. Theory 67(7) (2021) 4812-4827; Inverse Probl.…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due…
As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…
In this paper, a linearized semi-implicit finite difference scheme is proposed for solving the two-dimensional (2D) space fractional nonlinear Schr\"{o}dinger equation (SFNSE).The scheme has the property of mass and energy conservation on…
Automated segmentation of the optic cup and disk on retinal fundus images is fundamental for the automated detection / analysis of glaucoma. Traditional segmentation approaches depend heavily upon hand-crafted features and a priori…
Identifying out-of-distribution (OOD) data at inference time is crucial for many machine learning applications, especially for automation. We present a novel unsupervised semi-parametric framework COMBOOD for OOD detection with respect to…
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…
Corner detection is widely used in various computer vision tasks, such as image matching and 3D reconstruction. Our research indicates that there are theoretical flaws in Zhang et al.'s use of a simple corner model to obtain a series of…
Deep neural networks (DNNs) have achieved great success in the area of computer vision. The disparity estimation problem tends to be addressed by DNNs which achieve much better prediction accuracy in stereo matching than traditional…
Uncertainty quantification in medical images has become an essential addition to segmentation models for practical application in the real world. Although there are valuable developments in accurate uncertainty quantification methods using…
Graph Neural Networks (GNNs) have demonstrated remarkable efficacy in tackling a wide array of graph-related tasks across diverse domains. However, a significant challenge lies in their propensity to generate biased predictions,…
We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…
A distributed detection scheme where the sensors transmit with constant modulus signals over a Gaussian multiple access channel is considered. The deflection coefficient of the proposed scheme is shown to depend on the characteristic…