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We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
When solving noisy linear systems Ax = b + c, the theoretical and empirical performance of stochastic iterative methods, such as the Randomized Kaczmarz algorithm, depends on the noise level. However, if there are a small number of highly…
Reduced rank regression (RRR) is a fundamental tool for modeling multiple responses through low-dimensional latent structures, offering both interpretability and strong predictive performance in high-dimensional settings. Classical RRR…
Recent advancements in quantum computing, alongside successful deployments of quantum communication, hold promises for revolutionizing mobile networks. While Quantum Machine Learning (QML) presents opportunities, it contends with challenges…
Noise robust compressive sensing algorithm is considered. This algorithm allows an efficient signal reconstruction in the presence of different types of noise due to the possibility to change minimization norm. For instance, the commonly…
Quadratically-constrained basis pursuit has become a popular device in sparse regularization; in particular, in the context of compressed sensing. However, the majority of theoretical error estimates for this regularizer assume an a priori…
We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…
We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum…
A new geometrically-motivated algorithm for nonnegative matrix factorization is developed and applied to the discovery of latent "topics" for text and image "document" corpora. The algorithm is based on robustly finding and clustering…
In this paper, we present a novel optimization algorithm designed specifically for estimating state-space models to deal with heavy-tailed measurement noise and constraints. Our algorithm addresses two significant limitations found in…
We propose a new matrix factor model, named RaDFaM, which is strictly derived based on the general rank decomposition and assumes a structure of a high-dimensional vector factor model for each basis vector. RaDFaM contributes a novel class…
Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…
In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for the classification error. Minimax lower bounds are established to demonstrate the necessity of…
We present a general framework for designing efficient algorithms for unsupervised learning problems, such as mixtures of Gaussians and subspace clustering. Our framework is based on a meta algorithm that learns arithmetic circuits in the…
A class of recovering algorithms for 1-bit compressive sensing (CS) named Soft Consistency Reconstructions (SCRs) are proposed. Recognizing that CS recovery is essentially an optimization problem, we endeavor to improve the characteristics…
Integrating quantum key distribution (QKD) with existing optical networks is highly desired to reduce the deployment costs and achieve efficient resource utilization, and some pointtopoint transmitting experiments have verified its…
This paper considers a stochastic linear quadratic problem for discrete-time systems with multiplicative noises over an infinite horizon. To obtain the optimal solution, we propose an online iterative algorithm of reinforcement learning…
Quantum Machine Learning (QML) has emerged as a promising field that combines the power of quantum computing with the principles of machine learning. One of the significant challenges in QML is dealing with noise in quantum systems,…
The Broad Learning System (BLS) has gained significant attention for its computational efficiency and less network parameters compared to deep learning structures. However, the standard BLS relies on the pseudoinverse solution, which…
Flat regions of the neural network loss landscape have long been hypothesized to correlate with better generalization properties. A closely related but distinct problem is training models that are robust to internal perturbations to their…