相关论文: Debiasing Random Oblique Projections for Subsample…

Subsampled Randomized Hadamard Transform (SRHT), a popular random projection method that can efficiently project a $d$-dimensional data into $r$-dimensional space ($r \ll d$) in $O(dlog(d))$ time, has been widely used to address the…

In this work, we propose a method for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resilience in asynchronous systems. Specifically, we apply a…

Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, whose number, orientations, and dimensions are all unknown. In practice one may have access to…

Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…

Non-contrastive methods of self-supervised learning (such as BYOL and SimSiam) learn representations by minimizing the distance between two views of the same image. These approaches have achieved remarkable performance in practice, but the…

Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…

In this paper, we propose an abstract procedure for debiasing constrained or regularized potentially high-dimensional linear models. It is elementary to show that the proposed procedure can produce $\frac{1}{\sqrt{n}}$-confidence intervals…

The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and control. Traditionally, low-rank approximations are constructed…

Risk minimization for nonsmooth nonconvex problems naturally leads to first-order sampling or, by an abuse of terminology, to stochastic subgradient descent. We establish the convergence of this method in the path-differentiable case and…

We consider random sample splitting for estimation and inference in high dimensional generalized linear models, where we first apply the lasso to select a submodel using one subsample and then apply the debiased lasso to fit the selected…

We propose a novel modular debiasing technique applicable to any discrete random source, addressing the fundamental challenge of reliably extracting high-quality randomness from inherently imperfect physical processes. The method involves…

Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…

By exploiting the random sampling techniques, this paper derives an efficient randomized algorithm for computing a generalized CUR decomposition, which provides low-rank approximations of both matrices simultaneously in terms of some of…

Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

We develop a new randomized iterative algorithm---stochastic dual ascent (SDA)---for finding the projection of a given vector onto the solution space of a linear system. The method is dual in nature: with the dual being a non-strongly…

This paper presents a principled approach for detecting out-of-distribution (OOD) samples in deep neural networks (DNN). Modeling probability distributions on deep features has recently emerged as an effective, yet computationally cheap…

The dynamics in a primary Spectral Submanifold (SSM) constructed over the slowest modes of a dynamical system provide an ideal reduced-order model for nearby trajectories. Modeling the dynamics of trajectories further away from the primary…