相关论文: Fundamental Matrix Estimation: A Study of Error Cr…

We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…

The performance of algorithms for decentralized optimization is affected by both the optimization error and the consensus error, the latter of which arises from the variation between agents' local models. Classically, algorithms employ…

Determining whether two sets of images belong to the same or different distributions or domains is a crucial task in modern medical image analysis and deep learning; for example, to evaluate the output quality of image generative models.…

In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios…

We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate…

Sinopoli et al. (TAC, 2004) considered the problem of optimal estimation for linear systems with Gaussian noise and intermittent observations, available according to a Bernoulli arrival process. They showed that there is a "critical"…

In practical conjugate gradient (CG) computations it is important to monitor the quality of the approximate solution to $Ax=b$ so that the CG algorithm can be stopped when the required accuracy is reached. The relevant convergence…

Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental…

This paper applies the Recursive Projection Method (RPM) to the problem of finding the effective mechanical response of a periodic heterogeneous solid. Previous works apply the Fast Fourier Transform (FFT) in combination with various…

Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different…

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…

Bayesian matrix factorization (BMF) is a powerful tool for producing low-rank representations of matrices and for predicting missing values and providing confidence intervals. Scaling up the posterior inference for massive-scale matrices is…

Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has…

Self-supervised multi-frame depth estimation achieves high accuracy by computing matching costs of pixel correspondences between adjacent frames, injecting geometric information into the network. These pixel-correspondence candidates are…

We first study the generalization error of models that use a fixed feature representation (frozen intermediate layers) followed by a trainable readout layer. This setting encompasses a range of architectures, from deep random-feature models…

Animation data is often obtained through optical motion capture systems, which utilize a multitude of cameras to establish the position of optical markers. However, system errors or occlusions can result in missing markers, the manual…

We present a procedure for handling asymmetric errors. Many results in particle physics are presented as values with different positive and negative errors, and there is no consistent procedure for handling them. We consider the difference…

Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…

Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…

We present a simple randomized algorithm for approximate matrix multiplication (AMM) whose error scales with the *output* norm $\|AB\|_F$. Given any $n\times n$ matrices $A,B$ and a runtime parameter $r\leq n$, the algorithm produces in…