arXiv:2610.00498v1 Announce Type: cross Abstract: When minimizing the squared-error loss, the popular CP decomposition can be interpreted as parameter inference in a Gaussian model with a low-rank me...
arXiv:2607. 18209v1 Announce Type: cross Abstract: This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments.
arXiv:2607. 07008v1 Announce Type: cross Abstract: A common method for the representation and analysis of time-series data is the hidden Markov model (HMM), where each observation is associated with a hidden state that evolves over time.
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:2607. 27507v1 Announce Type: new Abstract: Matrix factorisation is a fundamental tool for exploiting low-dimensional structure in high-dimensional data, with applications such as data compression, denoising, structure discovery, interpretable representation learning, and dimensionality reduction.
arXiv:1811. 05336v2 Announce Type: replace-cross Abstract: Inference for factor models is often hampered by the lack of tractable and accurate variance estimates, which can materially distort downstream analyses.
arXiv:2608. 11917v1 Announce Type: new Abstract: Multi-output Gaussian process regression scales cubically in the number of observations times outputs, and dense kernel-matrix methods need bespoke handling whenever different outputs are observed at different inputs.
This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments. The joint distribution of the covariates may vary across environments, whereas the latent structure is decomposed into invariant factors with shared loadings and heterogeneous factors with environment-specific loadings.
arXiv:2410. 06329v4 Announce Type: replace-cross Abstract: Obtaining a reliable estimate of the joint probability mass function (PMF) of a set of random variables from observed data is a significant objective in statistical signal processing and machine learning.
arXiv:2610.07284v1 Announce Type: cross Abstract: Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising,...
arXiv:2607. 22262v1 Announce Type: cross Abstract: Modeling shared and subject-specific structure in multisubject spatiotemporal data remains challenging, particularly in neuroimaging, where both spatial and temporal patterns exhibit rich variability across subjects.
The paper introduces Sparse Separable Factor Analysis (SSFA), a latent factor model designed for complex-valued arrays that preserves amplitude and phase information. SSFA models each mode’s covariance with a low‑rank Hermitian factor structure plus a diagonal residual, applying element‑wise lasso penalties to achieve interpretable, phase‑preserving loadings via complex soft‑thresholding. The method is validated through simulations showing improved covariance estimation over vectorization approaches and applied to local field potential data from mice to compare separability across brain region, frequency, and time, as well as to impute missing recordings due to electrode misplacement.