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Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…
Federated learning (FL) is an emerging paradigm that allows a central server to train machine learning models using remote users' data. Despite its growing popularity, FL faces challenges in preserving the privacy of local datasets, its…
Recent advances have sparked significant interest in the development of privacy-preserving Principal Component Analysis (PCA). However, many existing approaches rely on restrictive assumptions, such as assuming sub-Gaussian data or being…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Causal structure learning has been extensively studied and widely used in machine learning and various applications. To achieve an ideal performance, existing causal structure learning algorithms often need to centralize a large amount of…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Principal Component Analysis (PCA) is a foundational technique in machine learning for dimensionality reduction of high-dimensional datasets. However, PCA could lead to biased outcomes that disadvantage certain subgroups of the underlying…
Federated Learning (FL) has gained significant recent attention in machine learning for its enhanced privacy and data security, making it indispensable in fields such as healthcare, finance, and personalized services. This paper…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…
As the modern world becomes increasingly digitized and interconnected, distributed signal processing has proven to be effective in processing its large volume of data. However, a main challenge limiting the broad use of distributed signal…
The alternating direction method of multipliers (ADMM) has been recently recognized as a promising optimizer for large-scale machine learning models. However, there are very few results studying ADMM from the aspect of communication costs,…
Kernel Principal Component Analysis (KPCA) is a key machine learning algorithm for extracting nonlinear features from data. In the presence of a large volume of high dimensional data collected in a distributed fashion, it becomes very…
In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations…
Given $n$ i.i.d. random matrices $A_i \in \mathbb{R}^{d \times d}$ that share a common expectation $\Sigma$, the objective of Differentially Private Stochastic PCA is to identify a subspace of dimension $k$ that captures the largest…
Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…
We study differentially private (DP) machine learning algorithms as instances of noisy fixed-point iterations, in order to derive privacy and utility results from this well-studied framework. We show that this new perspective recovers…
Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…