Conference

Rotation to a Sparse Structure using Lp Loss Functions: A Probabilistic Approach to Dimension Reduct

  • Inicio: February 5, 2025
  • Hora: 04:00 PM
  • Speaker: Gabriel Wallin | Lancaster University
  • Lugar: IMCA

Title: Rotation to a Sparse Structure using Lp Loss Functions: A Probabilistic Approach to Dimension Reduction

Abstract:

Factor analysis provides a probabilistic framework for dimension reduction by modeling observations in terms of a smaller number of latent factors. Unlike principal component analysis (PCA), which is based on maximizing variance along orthogonal directions, factor analysis explicitly accounts for measurement uncertainty and latent structure. However, the factor solution is not unique due to rotational indeterminacy - any rotation of the factors results in an equivalent model fit. We propose using Lp loss functions (0 < p <= 1) as rotation criteria to induce sparsity, enhancing interpretability of the latent factors. We establish theoretical properties, including consistency and uniqueness, and demonstrate that our method naturally arises as the limiting case of an Lp-regularized estimator. This work provides a principled approach to identifying interpretable low-dimensional structures in multivariate data.

Based on the following paper: https://link.springer.com/article/10.1007/s11336-023-09911-y