Related papers: Concentration inequalities for semidefinite least …
Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…
The success of self-supervised learning (SSL) has mostly been attributed to the availability of unlabeled yet large-scale datasets. However, in a specialized domain such as medical imaging which is a lot different from natural images, the…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
Ensuring reliable confidence scores from deep networks is of pivotal importance in critical decision-making systems, notably in the medical domain. While recent literature on calibrating deep segmentation networks has led to significant…
The appearance of singularities in the function of interest constitutes a fundamental challenge in scientific computing. It can significantly undermine the effectiveness of numerical schemes for function approximation, numerical…
In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by numerical experiments. Motivated by the recently popular…
In the domain of semi-supervised learning (SSL), the conventional approach involves training a learner with a limited amount of labeled data alongside a substantial volume of unlabeled data, both drawn from the same underlying distribution.…
Self-supervised learning (SSL) has emerged as a promising solution for addressing the challenge of limited labeled data in deep neural networks (DNNs), offering scalability potential. However, the impact of design dependencies within the…
Prior works have shown that semi-supervised learning algorithms can leverage unlabeled data to improve over the labeled sample complexity of supervised learning (SL) algorithms. However, existing theoretical analyses focus on regimes where…
Why is it that semidefinite relaxations have been so successful in numerous applications in computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance we note that…
In this work, we revisit dictionary-based sparse regression, in particular, Sequential Threshold Least Squares (STLS), and propose a score-guided library selection to provide practical guidance for data-driven modeling, with emphasis on…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
A set of high dimensional points $X=\{x_1, x_2,\ldots, x_n\} \subset R^d$ in isotropic position is said to be $\delta$-anti concentrated if for every direction $v$, the fraction of points in $X$ satisfying $|\langle x_i,v \rangle |\leq…
We model the cardinality-constrained portfolio problem using semidefinite matrices and investigate a relaxation using semidefinite programming. Experimental results show that this relaxation generates tight lower bounds and even achieves…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
Few shot segmentation (FSS) aims to learn pixel-level classification of a target object in a query image using only a few annotated support samples. This is challenging as it requires modeling appearance variations of target objects and the…
For a large class of optimization problems, namely those that can be expressed as finite-valued constraint satisfaction problems (VCSPs), we establish a dichotomy on the number of levels of the Lasserre hierarchy of semi-definite programs…
We introduce a generic technique to obtain linear relaxations of semidefinite programs with provable guarantees based on the commutativity of the constraint and the objective matrices. We study conditions under which the optimal value of…
While significant advances exist in pseudo-label generation for semi-supervised semantic segmentation, pseudo-label selection remains understudied. Existing methods typically use fixed confidence thresholds to retain high-confidence…
The data-compatibility approach to constrained optimization, proposed here, strives to a point that is "close enough" to the solution set and whose target function value is "close enough" to the constrained minimum value. These notions can…