Regularization Methods

Objectives

– Identify cases of statistical learning and inverse problems where regularization is useful: understand the motivations and objectives of penalization

– Know the most common regularization models and what reconstruction characteristics they promote, choose a regularization from the most common methods and estimate a regularized model using a gradient descent method

– Know and understand the different types of optimization problems and the algorithms used to solve them numerically

Course outline

– Main ingredients of inverse and statistical learning problems + practical examples

– Motivations and objectives of regularization

– Types of regularization and commonly encountered regularization functions

– Characterization of penalized problems: existence of solution, uniqueness, optimality conditions.

– Numerical methods to solve optimization problems

Prerequisites

Optimization, Python, Algebra