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Recently, Transformer-based text detection techniques have sought to predict polygons by encoding the coordinates of individual boundary vertices using distinct query features. However, this approach incurs a significant memory overhead and…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
In this paper we consider several problems concerning packet routing in distributed systems. Each problem is formulated using terms from Graph Theory and for each problem we present efficient, novel, algorithmic techniques for computing…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…
We investigate the problem of scanning and prediction ("scandiction", for short) of multidimensional data arrays. This problem arises in several aspects of image and video processing, such as predictive coding, for example, where an image…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
Machine learning pipelines that include a combinatorial optimization layer can give surprisingly efficient heuristics for difficult combinatorial optimization problems. Three questions remain open: which architecture should be used, how…
We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…
In this paper we present several novel efficient techniques and multidimensional data structures which can improve the decision making process in many domains. We consider online range aggregation, range selection and range weighted median…
We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…
The design of complex engineering systems leads to solving very large optimization problems involving different disciplines. Strategies allowing disciplines to optimize in parallel by providing sub-objectives and splitting the problem into…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
We consider a method of pairwise variations for smooth optimization problems, which involve polyhedral constraints. It consists in making steps with respect to the difference of two selected extreme points of the feasible set together with…
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline…
Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
We develop a theoretical framework for the analysis of oblique decision trees, where the splits at each decision node occur at linear combinations of the covariates (as opposed to conventional tree constructions that force axis-aligned…
Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…
We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either…
Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or…