By Mehar Bhasin
“Mathematics is the language with which God has written the universe.” Galileo Galilei
Artificial Intelligence is not magic; it’s just mathematics. The ideas behind thinking machines and the possibility to mimic human behavior are done with the help of mathematical concepts. In the recent weeks, I have received quite a few emails asking me just how much math is required in Artificial Intelligence. AI theory is a field that intersects statistical, probabilistic, computer science and algorithmic aspects arising from learning iteratively from data and finding hidden insights which can be used to build intelligent applications. A thorough mathematical understanding of many of these techniques is necessary for a good grasp of the inner workings of the algorithms and getting good results.
The mathematical foundations of AI consist of algebra, linear algebra, calculus, probability and statistics. Linear algebra is the most fundamental topic because data in machine learning is represented using matrices and vectors. Statistics are necessary to interpret results produced by learning algorithms and to understand data distributions. Calculus helps you understand how the learning process operates under the hood.
Algebra: Knowledge of algebra is perhaps fundamental to math in general. Besides mathematical operations like addition, subtraction, multiplication and division, you’ll need to know Exponents, Radicals, Factorials and Summations
Linear Algebra: Linear Algebra is the primary mathematical computation tool in Artificial Intelligence. You have to know what vectors and matrices are and how to perform basic operations on them such as addition, subtraction, and multiplication using dot products.
Statistics and Probability: This topic will probably take up a significant chunk of your time. Good news: these concepts aren’t difficult, so there’s no reason why you shouldn’t master them. You should understand the concept of a random variable, statistical independence, and conditional probability. Furthermore, you need to be able to calculate and interpret the mean, median variance, and standard deviation of a dataset. In terms of probability distributions, you need to know the normal distribution and the Binomial distribution. Understand p- values and confidence intervals.
Calculus: Calculus deals with changes in parameters, functions, errors and approximations. Working knowledge of multi-dimensional calculus is imperative in Artificial Intelligence. The most important concepts (albeit non-exhaustive) in Calculus
are (a) Derivatives — rules, hyperbolic derivatives and partial derivatives (b) Vector/Matrix Calculus — different derivative operators (and (c) Gradient
Algorithms — local/global maxima and minima, saddle points, convex functions, batches and mini-batches, stochastic gradient descent, and performance comparison.
Here are some videos which would be valuable for understanding key mathematical concepts related to Artificial Intelligence.
Machine Learning - Overview
This video shared an overview of Artificial Intelligence and its applications
Mathematics for Machine Learning
Here is a link to a no-nonsense guide (published by an AI Researcher Jason Dsouza) which covers all of the fundamentals of the math you’ll need to know.
This Edureka video on ‘Mathematics for Machine Learning’ teaches you all the math needed to get started with mastering Machine Learning. It teaches you all the necessary topics and concepts of Linear Algebra, Multivariate Calculus, Statistics, and Probability and also dives into the actual implementation of these topics.
Linear Algebra
This video covers the basics of linear algebra.
This video covers the core ideas from linear algebra that you need in order to do machine learning.
This video covers introduction to Matrix Methods in Data Analysis, Signal Processing, and Machine Learning by MIT Professor Strang
This video demonstrates matrix multiplication – the single most important and
widely-used mathematical operation in machine learning.
This video covers matrix determinants.
Basic Probability
This video covers probability review For AI
In this video, the instructor covers the core ideas from probability that you need in
order to do machine learning.
This video covers confidence interval review.
Advanced Probability
A series of videos giving an introduction to basic definitions, notation, and concepts.
Calculus
This video covers the core ideas from calculus that you need in order to do machine
learning.
This video covers Limits & Derivatives
This video provides specific examples of how calculus is applied in the real world, with an
emphasis on applications to machine learning.
It’s the mathematics that creates magic behind all inventions. So, to lead in
today’s AI-driven world, you need to have a great flair in math.