Related papers: SubApSnap: Solving parameter-dependent linear syst…

A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…

Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…

We study the fundamental problem of sampling independent events, called subset sampling. Specifically, consider a set of $n$ events $S=\{x_1, \ldots, x_n\}$, where each event $x_i$ has an associated probability $p(x_i)$. The subset sampling…

Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…

Background: Photoacoustic Microscopy (PAM) integrates optical and acoustic imaging, offering enhanced penetration depth for detecting optical-absorbing components in tissues. Nonetheless, challenges arise in scanning large areas with high…

Solving a linear system $Ax=b$ is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are…

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…

We provide fast algorithms for overconstrained $\ell_p$ regression and related problems: for an $n\times d$ input matrix $A$ and vector $b\in\mathbb{R}^n$, in $O(nd\log n)$ time we reduce the problem $\min_{x\in\mathbb{R}^d} \|Ax-b\|_p$ to…

A recurring pattern in "reasoning without training" is that base LLMs already assign non-trivial probability mass to correct multi-step solutions; the bottleneck is locating these modes efficiently at inference time. Power sampling provides…

Subset selection from massive data with noised information is increasingly popular for various applications. This problem is still highly challenging as current methods are generally slow in speed and sensitive to outliers. To address the…

We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…

A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…

We propose subsampling as a unified algorithmic technique for submodular maximization in centralized and online settings. The idea is simple: independently sample elements from the ground set, and use simple combinatorial techniques (such…

Accuracy at the top is a special class of binary classification problems where the performance is evaluated only on a small number of relevant (top) samples. Applications include information retrieval systems or processes with manual…

When approaching to problems in computer science, we often encounter situations where a subset of a finite set maximizing some utility function needs to be selected. Some of such utility functions are known to be approximately submodular.…

Optimization with time-dependent partial differential equations (PDEs) as constraints {appears} in many science and engineering applications. The associated first-order necessary optimality system consists of one forward and one backward…

We describe a numerical framework that uses random sampling to efficiently capture low-rank local solution spaces of multiscale PDE problems arising in domain decomposition. In contrast to existing techniques, our method does not rely on…

In this work, we study how to use sampling to speed up mechanisms for answering adaptive queries into datasets without reducing the accuracy of those mechanisms. This is important to do when both the datasets and the number of queries asked…

Snapshot compressive imaging (SCI) aims to capture the high-dimensional (usually 3D) images using a 2D sensor (detector) in a single snapshot. Though enjoying the advantages of low-bandwidth, low-power and low-cost, applying SCI to…