arXiv Machine Learning
A Functional SVD Framework for Regularized Multivariate Functional PCA with Dual Penalization
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arXiv Statistics ML
Sep 4
Online Learning of Functional Principal Component Analysis for Multidimensional Functional Data
The paper introduces an online framework for functional principal component analysis (FPCA) tailored to multidimensional functional data streams. It models functional principal components with tensor product splines, enforcing smoothness and orthonormality via a penalized approach on a Stiefel manifold. The authors present efficient Riemannian stochastic gradient descent and AdaGrad algorithms, along with a dynamic smoothing parameter tuning strategy based on rolling block validation, and provide asymptotic normality results and confidence intervals for the estimators.
arXiv Machine Learning
Sep 30
High-Dimensional Partial Least Squares: Spectral Analysis and Fundamental Limitations
The paper investigates Partial Least Squares (PLS) in high-dimensional settings, focusing on a model where two data matrices share a low-rank latent structure plus individual-specific components. By analyzing the singular vectors of the cross‑covariance matrix with random matrix theory, the authors derive asymptotic characterizations of how well the estimated latent directions align with the true ones. They show that the PLS variant based on Singular Value Decomposition (PLS‑SVD) outperforms separate principal component analysis in detecting the common latent subspace, while also identifying regimes where PLS‑SVD behaves counter‑intuitively or reaches fundamental limits.
arXiv Machine Learning
Oct 5
Kernel Singular Value Decomposition with Extension to Multiple Data Sources
Kernel Singular Value Decomposition (KSVD) learns singular vectors for an asymmetric kernel matrix derived from two data sources. The paper extends KSVD to multiple data sources, introducing eKSVD, which jointly learns nonlinear feature mappings and captures maximal information across all sources while incorporating pair‑wise couplings. The authors derive a dual optimization framework, a covariance‑based approach, and demonstrate the effectiveness of eKSVD and neural‑network‑based feature mappings through numerical experiments.
arXiv Statistics ML
Sep 18
Robust Multi-Task Learning for Principal Component Analysis
The paper introduces robust multi-task procedures for principal component analysis that leverage similarity across tasks to enhance eigenspace estimation while remaining resilient to outlier tasks. It establishes non-asymptotic convergence rates and demonstrates that the methods achieve minimax optimal performance across various regimes. One procedure, based on matrix-depth, attains optimal error dependence on the proportion of outlier tasks, addressing a key challenge in robust multi-task learning.
arXiv Machine Learning
Jul 7
msPCA: An R Package for Sparse PCA with Multiple Components
arXiv:2607. 05229v1 Announce Type: cross Abstract: We present msPCA: an open-source R package for sparse principal component analysis with multiple components.
arXiv Machine Learning
Jun 3
A Robust Optimization Approach to Sparse Principal Component Analysis
arXiv:2606. 03553v1 Announce Type: cross Abstract: While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data.