Related papers: Squeezed Covariance Matrix Estimation: Analytic Ei…
We propose a sequential quadratic programming (SQP) algorithm for inequality constrained optimization that is robust to the presence of bounded noise in function and derivative evaluations. We cover the case where constraint evaluations…
Segmentation evaluation metrics traditionally rely on binary decision logic: predictions are either correct or incorrect, based on rigid IoU thresholds. Detection--based metrics such as F1 and mAP determine correctness at the object level…
Individual patient data (IPD) are essential for statistical inference in clinical research. However, privacy concerns, high data-sharing costs, and restrictive access often make IPD unavailable. Conventional synthetic data generation…
Nonlinear eigenvalue equations arise naturally in quantum information theory, particularly in the variational quantification of entanglement. In this work, we present a hybrid analytical and numerical framework for evaluating the geometric…
Evaluating the quality of synthetic data remains a key challenge for ensuring privacy and utility in data-driven research. In this work, we present an evaluation framework that quantifies how well synthetic data replicates original…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
Self-supervised learning (SSL) has shown impressive results in downstream classification tasks. However, there is limited work in understanding their failure modes and interpreting their learned representations. In this paper, we study the…
We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…
This study explores a detailed examination of various classes of single- and two-mode Gaussian states as key elements for an estimation process, specifically targeting the evaluation of an unknown squeezing parameter encoded in one mode. To…
The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such…
Integer Quadratic Programming (IQP), $\min\{x^T Q x + c^T x : Ax \le b,\, x\in\Z^n\}$, is a fundamental problem in combinatorial optimization. While the convex and concave special cases admit polynomial-time algorithms for fixed~$n$, the…
This work aims to provide both privacy and utility within a split learning framework while considering both forward attribute inference and backward reconstruction attacks. To address this, a novel approach has been proposed, which makes…
By enabling multiple agents to cooperatively solve a global optimization problem in the absence of a central coordinator, decentralized stochastic optimization is gaining increasing attention in areas as diverse as machine learning,…
We study online statistical inference for the solutions of stochastic optimization problems with equality and inequality constraints. Such problems are prevalent in statistics and machine learning, encompassing constrained $M$-estimation,…
We study the classification problem for high-dimensional data with $n$ observations on $p$ features where the $p \times p$ covariance matrix $\Sigma$ exhibits a spiked eigenvalue structure and the vector $\zeta$, given by the difference…
Repeating a gate sequence multiple times amplifies systematic errors coherently, making it a useful tool for characterizing quantum gates. However, the precision of such an approach is limited by low-frequency noises, while its efficiency…
In this paper we develop a complete analytical framework based on Random Matrix Theory for the performance evaluation of Eigenvalue-based Detection. While, up to now, analysis was limited to false-alarm probability, we have obtained an…
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can…
The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…