Heavy-Tailed Distribution Modeling

Background: The Fern model’s transport structure supports exact inference for any elliptically contoured distribution, including multivariate Student-t, Cauchy, and Laplace distributions, because its map is an affine composition of shift, rotate, and scale operations.

Question / Future Work: Investigate the explicit application and validation of the Noise Titration protocol using the base Fern architecture to model heavy-tailed distributions, such as the multivariate Student-t or Laplace distributions, by substituting the base Gaussian noise profile with these heavier-tailed profiles. This requires extending the framework beyond the current focus on Gaussian inference.