Related papers: Structural Conditions for Projection-Cost Preserva…
We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…
Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to…
Random Projections have been widely used to generate embeddings for various graph learning tasks due to their computational efficiency. The majority of applications have been justified through the Johnson-Lindenstrauss Lemma. In this paper,…
It is often desirable to reduce the dimensionality of a large dataset by projecting it onto a low-dimensional subspace. Matrix sketching has emerged as a powerful technique for performing such dimensionality reduction very efficiently. Even…
Low Rank Approximation (LRA) of a matrix is a hot research subject, fundamental for Matrix and Tensor Computations and Big Data Mining and Analysis. Computations with low rank matrices can be performed at sublinear cost -- by using much…
Low-rank structure have been profoundly studied in data mining and machine learning. In this paper, we show a dense matrix $X$'s low-rank approximation can be rapidly built from its left and right random projections $Y_1=XA_1$ and…
We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
We study the problem of structured prediction under test-time budget constraints. We propose a novel approach applicable to a wide range of structured prediction problems in computer vision and natural language processing. Our approach…
We consider a framework for structured prediction based on search in the space of complete structured outputs. Given a structured input, an output is produced by running a time-bounded search procedure guided by a learned cost function, and…
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…
Applications in machine learning and data mining require computing pairwise Lp distances in a data matrix A. For massive high-dimensional data, computing all pairwise distances of A can be infeasible. In fact, even storing A or all pairwise…
Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…
The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a…
One of the main difficulties in micromagnetics simulation is the norm preserving constraints $\|\mathbf{m}\|=1$ at the continuous or the discrete level. Another difficulty is the stability with the time step constraint. Using standard…
This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and…
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are…
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
A simple formula is proved to be a tight estimate for the condition number of the full rank linear least squares residual with respect to the matrix of least squares coefficients and scaled 2-norms. The tight estimate reveals that the…