Regularization: Promoting Optimal Solutions

This lecture covers the concept of regularization in the context of least-squares problems. Regularization is introduced as a tool to address challenges such as non-uniqueness of solutions, ill-conditioning, and over-fitting. The lecture explains how regularization promotes solutions with smaller norms, alleviates ill-conditioning by stabilizing the solution, and counters over-fitting by constraining the solution space. The use of l2-regularization, also known as ridge regression, is detailed, along with its impact on the solution's norm. The lecture also discusses the role of regularization in ensuring consistency with prior models and the trade-off between bias and variance in the regularized risk.