USE OF LINEAR ALGEBRA AND PARTIAL DERIVATIVES IN SUPERVISED LEARNING (ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING)

Abstract

When we talk about new technologies and the advancement in the field of Computer Science, the first thing that comes to our mind is Artificial Intelligence and Machine Learning. Artificial Intelligence has seen resurgence in the 21st century because of its ability to mimic functions done by human intelligence like “problem solving” and “learning”. It is slowly becoming the area of interest of the new generation because of its modern capabilities which even human intelligence struggle to perform like competing at highest level in strategic game systems, intelligent routing, operating cars autonomously and simulations. Artificial Intelligence may look easy but there are several tools involved in making it successful. One of the main tool is “Statistical Methods”. Linear algebra and Partial Differential Equations have become the base of this field. The objective of our paper is to throw light on how Statistical Methods and Mathematical optimization provide the base for the working of Supervised Learning. Over years, algorithms inspired by Partial Differential Equations (PDE) and Linear Algebra have had an immense impact on many processing and autonomously performed tasks that involve speech, image and video data. Image processing tasks and intelligent routing done using PDE models has lead to ground-breaking contributions. The reinterpretation of many modern machine capabilities like artificial neural networks through PDE lens has been creating multiple celebrated approaches that benefit a vast area. In this paper, we have established some working of these methods in different subfields of Artificial Intelligence. Guided by well-established theories we demonstrate new insights and algorithms for Supervised Learning and demonstrate the competitiveness of different numerical experiments used in the sub-fields. Not only will we see the wide application of Artificial intelligence but also its ability to slowly replace human works leading to unemployment which are part of its limitation. This research will provide wider insights into the multiple mathematical processes which acts as roots to make the field of Computer Science interesting and successful.