Machine learning is a deep and complex topic that encompasses statistical, probabilistic, computer science and algorithmic concepts. By understanding machine learning, engineers are able to identify hidden insights within data and build more intelligent software.
But for aspiring machine learning professionals, it can be hard to know where to start. Especially with the level of mathematical understanding required.
You need to know what’s going on under the hood of your systems to ensure you get good results. And for that, you need to be able to select the right algorithm, choose parameter settings and validation strategies. Not to mention calculating confidence interval and uncertainties, among other things.
There are different levels of maths required for each of these techniques. And there are many arguments as to how much math you actually need in the industry. But to be able to study machine learning theory in an academic setting, you’ll need high level math.
Luckily, there are plenty of exceptional resources you can explore to get the knowledge you need. And since each persons learning preference is different, we’ve included a mixture of resources below. All of which can help you effectively learn mathematics for machine learning.
Read Books and Papers on Mathematics for Machine Learning
To get to grips with the advanced math required for machine learning concepts, you’ll need to find specialised resources. The detailed knowledge you need won’t be covered in your typical math book. So it’s best to locate a number of books and papers that will help cover the areas required. Some are great as a starting point, and others are ideal for the more advanced topics.
A few that have been rated highly by machine learning professionals and enthusiasts online are:
A great starting point as the two halves of the book take you from mathematical foundations through to advanced topics. In the first half you’ll cover key linear algebra and calculus concepts. Then the second half narrows the focus to machine learning mathematics where you’ll explore regression, dimensionality reduction and support vector machines. The authors wrote this with the intention of it equipping you with the skills to read more advanced books.
Another great choice for familiarisation with machine learning math-related concepts, that’s also heavily referenced in academia. It assumes no prior knowledge of pattern recognition or machine learning concepts. Plus, it covers recent developments in detail such as probabilistic graphical models and deterministic inference methods.
It’s estimated that around 80% of your time as a machine learning data scientist is spent on data preparation. So this book focuses on data and uncertainty while emphasising mathematical methods and their conceptual underpinnings. As opposed to their theoretical properties. After reading, you’ll be more comfortable with topics like estimators and statistical significance.
In your machine learning career you need to build probabilistic models. This requires you to be confident with probability theory concepts such as conditional probability and different probability distributions. This book focuses on probability theory and its conventional mathematics. However, it is viewed in a wider context than that of standard textbooks.
This paper aims to explain the entire matrix calculus required to understand the training of deep neural networks. Which is important since in deep learning you must be knowledgeable of many fundamental matrix operations.
This book is favoured for its progressively advanced take on deep learning. In it you will explore the mathematics of multilayer perceptrons, convolutional neural networks (CNN), and recurrent neural networks (RNN). It also introduces you to other essential concepts like regularisation (L1 and L2 norm) and dropout layers.
Take a course dedicated to gaining math skills
Specialised books and papers do an excellent job of providing you with extensive detailed knowledge of machine learning math. But if you want to make your introduction to learning a little easier, there are some excellent online courses available.
A particular favourite of those researching machine learning math are those from the Khan Academy. Where a comprehensive collection of free online videos are provided to explain numerous math topics. The courses are not aimed at machine learning, but many of the topics discussed are highly relevant.
Their linear algebra course, for example, teaches you essential knowledge about coordinate systems, linear transformations, matrix transformations and vector spaces. The examples of 2D and 3D graphic systems are easily visualised compared to the multidimensional spaces of machine learning problems. Plus, there are topics covered that are important in machine learning like square calculations and eigenvectors.
As the prerequisite for machine learning in industry is data analysis, there are also courses to help you with statistics. These short courses in Descriptive Statistics, Inferential Statistics, Data Science and Mastering Data Analysis would all be helpful. As they cover some of the key concepts required for data science and machine learning like random variables and distributions.
You could also find online courses dedicated to calculus. The Khan Academy provides ones on precalculus, differential calculus and integral calculus. Plus, a multivariable calculus course which covers topics like gradient descent and partial derivatives, which are central to deep learning.
These courses and many more available online will help you get comfortable with these mathematical concepts. Allowing you to find your feet before diving into the more intense and focused resources on mathematics for machine learning.
The best way to become good at math is to practice using it regularly. Once you’re ready to take the next step in your machine learning journey, we can help. Stonebridge Associated Colleges provides an online Access to Higher Education Diploma (Computer Science and Maths).
As machine learning is a specialised field in computer science, this course teaches you essential knowledge of machine learning principles.
It will also help you develop your skills in mathematics. Allowing you to explore advanced topics like calculus, algebraic methods and trigonometry. Which underpin many computing and programming concepts.
Modules such as statistics will also be highly valuable to you, better preparing you for your degree.
Access to HE Diplomas are a Level 3 qualification. So are an excellent alternative to A Level study. You can gain the subject specific knowledge you need to study computer science and machine learning at university.
If you’re ready, take the next step to become a machine learning professional by clicking the link below.