arXiv:2505. 19925v2 Announce Type: replace-cross Abstract: The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers.
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The paper introduces a new dimensionality reduction technique that enhances nearest‑neighbour relationships to estimate high‑information projections. It constructs a matrix encoding local covariance via nearest‑neighbour pairs and shows that, under standard regularity conditions, this matrix consistently estimates the Density Information Matrix (DIM), a non‑parametric analogue of the Fisher Information Matrix. The authors also demonstrate the method’s practical usefulness for clustering and outlier detection.
arXiv:2603.25911v2 Announce Type: replace-cross Abstract: Tensor-on-tensor regression is an important tool for the analysis of tensor data, aiming to predict a set of response tensors from a correspo...
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.
The paper introduces a multivariate pseudo‑Voigt mixture model, combining Gaussian and Cauchy components with shared location and scale parameters, for robust clustering and outlier detection. Parameter estimation is performed using an EM algorithm that leverages latent variables for efficient likelihood inference. The authors evaluate the model through simulations and real data, comparing it to established robust mixtures such as contaminated normals, and demonstrate its effectiveness on heavy‑tailed datasets.
The paper introduces a method for clustering matrix-variate normal data that accounts for outliers. It extends the OCLUST algorithm by employing subset log-likelihood distributions and an iterative trimming procedure. This approach enables robust clustering of complex structured data such as images and time series.
arXiv:2606. 06233v1 Announce Type: cross Abstract: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques.