This is an essay I've submitted as a part of my Second Year mathematics course at Warwick, @2019
Recently, both research and industry face many problems where the objective is to 'guess' a function of multiple variables (features) based on its values at particular points (test samples). This essay focuses on two approaches, first linear multiple regression is discussed with rigorous algebraic background. It presents a proof of uniqueness of the optimal solution is proven and points towards ways of computing it through Moore-Penrose pseudoinverse.
In the second part limitations of such a model are illustrated and an alternative in the form of a neural network is presented. Difficulties in finding the optimal parameters are briefly discussed and a numerical solution together with a Back Propagation algorithm are derived.