Σεμινάριο: "Statistical Estimation with a Penalty and its Geometry"

ΚΥΚΛΟΣ ΣΕΜΙΝΑΡΙΩΝ ΣΤΑΤΙΣΤΙΚΗΣ 2025-2026

Ομιλητής: Piotr Graczyk, Professor, Université d'Angers, France

Statistical Estimation with a Penalty and its Geometry

Αίθουσα: ΤΒΑ

ΠΕΡΙΛΗΨΗ

We consider the regression problem Y = Xb + ε where X is the matrix with data on p variables observed n times, Y the response vector, and ε an error. The coefficient vector b is unknown and must be estimated. In classical statistics we have n ≥ p and we use an ordinary least squares (OLS) estimator. In modern statistics we need to consider the case n < p of Big Data. The OLS is then penalized. The famous LASSO estimator uses the ℓ1 penalty. Modern Statistics requires other penalties. Surprising links between the pattern discovered by an estimator with a polyhedral penalty p and the geometry of the dual ball B∗ will be explained. For ℓ1 penalty the dual ball B∗ is a cube. For other penalties, the convex polyhedron B∗ is different, e.g. a signed permutahedron for the sorted ℓ1 penalty.