Related papers: SubApSnap: Solving parameter-dependent linear syst…
The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…
A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…
Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples…
The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…
A fast and stable algorithm for estimating multidimensional adaptive P-spline models is presented. We call it as Separation of Overlapping Penalties (SOP) as it is an extension of the \textit{Separation of Anisotropic Penalties} (SAP)…
We consider the reconstruction problem of video snapshot compressive imaging (SCI), which captures high-speed videos using a low-speed 2D sensor (detector). The underlying principle of SCI is to modulate sequential high-speed frames with…
Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…
We present a technique using data depth functions and resampling to perform best subset variable selection for a wide range of statistical models. We do this by assigning a score, called an $e$-value, to a candidate model, and use a fast…
Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…
In this paper, we propose a new approach to model reduction of parameterized partial differential equations (PDEs) based on the concept of adaptive reduced bases. The presented approach is particularly suited for large-scale nonlinear…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
We present classical sublinear-time algorithms for solving low-rank linear systems of equations. Our algorithms are inspired by the HHL quantum algorithm for solving linear systems and the recent breakthrough by Tang of dequantizing the…
Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
Gradient-based meta-learning techniques aim to distill useful prior knowledge from a set of training tasks such that new tasks can be learned more efficiently with gradient descent. While these methods have achieved successes in various…
Integral linear systems $Ax=b$ with matrices $A$, $b$ and solutions $x$ are also required to be in integers, can be solved using invariant factors of $A$ (by computing the Smith Canonical Form of $A$). This paper explores a new problem…
We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…
Subsampling is a computationally efficient and scalable method to draw inference in large data settings based on a subset of the data rather than needing to consider the whole dataset. When employing subsampling techniques, a crucial…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…