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We present a federated, asynchronous, and $(\varepsilon, \delta)$-differentially private algorithm for PCA in the memory-limited setting. Our algorithm incrementally computes local model updates using a streaming procedure and adaptively…

Principal Component Analysis (PCA) is a widely used method for dimensionality reduction, but it often overlooks fairness, especially when working with data that includes demographic characteristics. This can lead to biased representations…

Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the…

Distributed aggregative optimization methods are gaining increased traction due to their ability to address cooperative control and optimization problems, where the objective function of each agent depends not only on its own decision…

Differentially private (DP) tabular data synthesis generates artificial data that preserves the statistical properties of private data while safeguarding individual privacy. The emergence of diverse algorithms in recent years has introduced…

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

We propose a novel single-loop decentralized algorithm called DGDA-VR for solving the stochastic nonconvex strongly-concave minimax problem over a connected network of $M$ agents. By using stochastic first-order oracles to estimate the…

The paper studies the distributed stochastic compositional optimization problems over networks, where all the agents' inner-level function is the sum of each agent's private expectation function. Focusing on the aggregative structure of the…

A representative model in integrative analysis of two high-dimensional correlated datasets is to decompose each data matrix into a low-rank common matrix generated by latent factors shared across datasets, a low-rank distinctive matrix…

A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier…

During the past two decades, multi-agent optimization problems have drawn increased attention from the research community. When multiple objective functions are present among agents, many works optimize the sum of these objective functions.…

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 efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochastic Galerkin approach, the solutions are represented as…

A key factor in developing high performing machine learning models is the availability of sufficiently large datasets. This work is motivated by applications arising in Software as a Service (SaaS) companies where there exist numerous…

Many commonly used learning algorithms work by iteratively updating an intermediate solution using one or a few data points in each iteration. Analysis of differential privacy for such algorithms often involves ensuring privacy of each step…

Multi-block CCA constructs linear relationships explaining coherent variations across multiple blocks of data. We view the multi-block CCA problem as finding leading generalized eigenvectors and propose to solve it via a proximal gradient…

This paper delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on…

Dantzig-Wolfe decomposition (DWD) is a classical algorithm for solving large-scale linear programs whose constraint matrix involves a set of independent blocks coupled with a set of linking rows. The algorithm decomposes such a model into a…

Decentralized and federated learning algorithms face data heterogeneity as one of the biggest challenges, especially when users want to learn a specific task. Even when personalized headers are used concatenated to a shared network…

Differential privacy enables organizations to collect accurate aggregates over sensitive data with strong, rigorous guarantees on individuals' privacy. Previous work has found that under differential privacy, computing multiple correlated…