Introduction to the LASSO A Convex Optimization Approach for High-dimensional Problems

The term ‘high-dimensional’ refers to the case where the number of unknown parameters to be estimated, p, is of much larger order than the number of observations, n, that is p ≫ n. Since traditional statistical methods assume many observations and a few unknown variables, they can not cope up with the situations when p ≫ n. In this article, we study a statistical method, called the ‘Least Absolute Shrinkage and Selection Operator’ (LASSO), that has got much attention in solving high-dimensional problems. In particular, we consider the LASSO for high-dimensional linear regression models. We aim to provide an introduction of the LASSO method as a constrained quadratic programming problem, and we discuss the convex optimization based approach to solve the LASSO problem. We also illustrate applications of LASSO method using a simulated and a real data examples. © 2018, Indian Academy of Sciences.