Mathematics for Machine Learning — Basic Guide with adjunctive resources

Mathematics and Machine Learning share a lot of aspects and common goals to use data to improve decisions.

Mathematics for Machine Learning — Basic Guide with adjunctive resources
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Mathematics is exceedingly useful for developing intelligent systems that can take decisions autonomously. There are many reasons the Mathematics of Machine Learning is critical for the success of ML models and engineering automated systems.

Machine Learning is ubiquitous, but learning the low-level technical concepts which require background in mathematics and statistics is often abstracted away from the learners because of hype marketing and improper roadmaps. This brings with it the danger that the learners become unaware of pre-requisite knowledge and experience only uncomfortable events while learning.

We know the options out there; prerequisites and the Math skills you need to become a successful in ML and AI job roles.

In reality, learning mathematics for machine learning can be intimidating, as it is extremely concerned with finite sample analysis, model mis-specification, and computational considerations. Therefore, a thorough mathematical understanding is not an option for a career in Machine Learning and AI.

If this sounds intimidating already, don't make assumptions yet. The libraries and software packages make machine learning much easier today than it was 10 years ago. You need to start with the essential concepts first to build the required mathematical intuition to grow from one level of understanding to another.

In this guide, you'll find brief explanations chained with adjunctive resources that provide mathematically rigorous introduction to the important concepts to help you gain the pre-requisite knowledge for learning Machine Learning, Deep Learning and AI.

Essential Math for Machine Learning

These mathematics concepts are required to become a successful Machine Learning Engineer/ Scientist.

note: we have added adjunctive courses in each section


Linear Algebra

Linear Algebra is the fundamental and most important mathematical topics underpinning Machine Learning. Linear algebra is applied in machine learning algorithms and enables ML algorithms to work in loss functions, regularisation, covariance matrices, Singular Value Decomposition (SVD), Matrix Operations, and support vector machine classification.

It is broadly used in developing algorithms that support machine learning systems like neural networks and the backpropagation to train deep learning neural networks.

Linear algebra solves the problem of representing data and computations in ML models. It is concerned with vectors, matrices, and linear transforms.

As a beginner, you need to learn the fundamental concepts such as linear systems, vectors, matrix algebra and solution sets that will cement your knowledge to apply these concepts to machine learning.

Linear algebra is hard. Here are a few of the best resources that cover matrix theory and linear algebra, emphasizing topics in the context of data science and machine learning.


Calculus

As a machine learning engineer, you must have a good understanding of calculus. The basic knowledge of calculus will help you understand how functions change over time (derivatives), and to calculate the total amount of a quantity that accumulates over a time (integrals).

Calculus is the language for modeling behaviours, helping to understand ML techniques, such as:

  • Backpropagation in neural networks
  • Regression using optimal least square
  • Expectation maximization in fitting probability models

It's easier to learn calculus to improve your understanding and application of machine learning.

You must have a basic knowledge of calculus to keep in step with the progress of your machine learning career. The basics will first help you read and understand the most basic equations that enable you to speak precisely about the properties of functions and better understand their behaviour. In simple words, calculus is the perfect tool you need to describe and to understand the progress of how machines learn.

The three key areas of calculus that we recommend for beginners to focus on are:

  • Differentiation
  • Vector Calculus
  • Optimization

Normally, taking a calculus course involves doing lots of labor and calculations, but having some experience in Python or R can make the process efficient and much more fun. Here are some of the best learning resources.


Probability and Distributions

Probability and distributions are the basic building block of machine learning.

Probability distribution is a mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.

It is widely used for hypothesis testing and for drawing conclusions on a population from a small sample. In machine learning, statistical inferences use probability distribution of data to analyze and predict trends.

As a beginner, you must be familiar with the following probability distributions:

  • Binomial distribution
  • Poisson distribution
  • Normal
  • Exponential
  • Chi-square

If you are learning math for machine learning, then learning statistics along with programming should be the first step. We have created a few basic study guides for data science learners and all topics in the context of machine learning.


Linear Regression

Linear regression is one of the most popular and well understood algorithms in statistics and machine learning, commonly used for predictive analysis and modeling.

Linear regression analysis supports supervised machine learning tasks of learning a function that maps an input to an output based on example input-output pairs. In simple words, we can predict the output values for new data based on relationships from the previous data sets. This method is used for forecasting and finding out cause-and-effect relationship between variables.

Linear Regression is an algorithm that every Machine Learning engineer must know. It is a simple yet powerful ML algorithm.

Learn different methods, and how to select features to make predictions using the linear regression machine learning model.

  • Simple Linear Regression
  • Ordinary Least Squares
  • Gradient Descent
  • Regularization

Linear regression is essential to understand as it is one of the most common statistical modeling approaches in machine learning and the following resources will teach you how to implement linear regression.


Dimensionality Reduction

It is difficult to work with high-dimensional data because it is characterized by multiple dimensions. In simple words, High dimension is when variable numbers p is higher than the sample sizes n, i.e. p>n, cases.

The best example of high-dimensional data is imaging data, and it comes with various complications. It is very difficult to analyze high-dimensional data; the visualization is nearly inconceivable, and the storage of the data vectors is expensive.

We've all heard the term Big Data. This term has a very reasonable meaning when you get to the point where the large number of data points force you to use different methods.

What then is high-dimensional data but data that has many dimensions, variables, features, columns, etc. For instance, the imaging data will have giant datasets with many data points that have many variables and dimensions. In other words, Big Data is high-dimensional data.

The curse of high-dimensional data is that there are far too many variables, so there is a need for performing dimension analysis, reducing dimensions in data, feature selection and plenty more techniques for optimizing the performance of our models, saving training time, cost, and visualizing the results of ML models.

There are popular techniques used for dimensionality reduction, such as:

  • Principal Component Analysis (PCA)
  • t-Distributed Stochastic Neighbor Embedding (t-SNE)
  • Linear Discriminant Analysis (LDA)
  • Generalized Discriminant Analysis (GDA)
  • IsoMap
  • Autoencoders.

We recommend for beginners to become acquainted with Principal Component Analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) for unsupervised learning.

Here are a few of the best free resources we’ve found for learning Dimensionality reduction for Machine Learning and Data Science.


Conclusion

Behind every Machine Learning success, there is mathematics and statistics.

The basic concepts we explained in this guide can be difficult to learn for someone only familiar with Arithmetic. Understanding these concepts is essential to learning the applications of Machine Learning to secure an entry-level job.

If you want to learn machine learning, you’ll have to think on your feet to learn mathematics. The adjunctive resources will help you build the right math skills to work with complex machine learning algorithms.

Your Guide to Machine Learning Career

We hope your journeys will go as you hope, and that the resources listed in this article will equip you for Mathematical Thinking.

Thanks for making it to the end

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Important References:

OCW MIT: https://ocw.mit.edu/courses/18-657-mathematics-of-machine-learning-fall-2015/

Cambridge University Press: https://mml-book.github.io/


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