Tag: pca
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Combinatorial Sparse PCA Beyond the Spiked Identity Model
Combinatorial Sparse PCA Beyond the Spiked Identity Model arXiv:2603.02607v1 Announce Type: new Abstract: Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance $Sigma$, whose top eigenvector $v in R^d$ is $s$-sparse. Existing sparse PCA algorithms can be broadly categorized into…
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PCA++: How Uniformity Induces Robustness to Background Noise in Contrastive Learning
PCA++: How Uniformity Induces Robustness to Background Noise in Contrastive Learning arXiv:2511.12278v1 Announce Type: new Abstract: High-dimensional data often contain low-dimensional signals obscured by structured background noise, which limits the effectiveness of standard PCA. Motivated by contrastive learning, we address the problem of recovering shared signal subspaces from positive pairs, paired observations sharing the same…
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An Iterative Algorithm for Differentially Private $k$-PCA with Adaptive Noise
An Iterative Algorithm for Differentially Private $k$-PCA with Adaptive Noise arXiv:2508.10879v1 Announce Type: new Abstract: 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 variance directions of $Sigma$, while…
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Exponential Convergence of CAVI for Bayesian PCA
Exponential Convergence of CAVI for Bayesian PCA arXiv:2505.16145v1 Announce Type: new Abstract: Probabilistic principal component analysis (PCA) and its Bayesian variant (BPCA) are widely used for dimension reduction in machine learning and statistics. The main advantage of probabilistic PCA over the traditional formulation is allowing uncertainty quantification. The parameters of BPCA are typically learned using…