The Essential Math Behind Machine Learning: What Topics You Really Need to Know

Machine learning is everywhere these days. It powers recommendations on Netflix, the magic behind voice assistants, and even life-saving tools in healthcare. But while it may seem like magic, at its core, machine learning is built on some pretty solid math.

If you’re new to the field, it might feel like you need a Ph.D. to understand it all. The good news? You don’t. However, having a grasp of a few key mathematical concepts can make a world of difference in truly understanding how machine learning works. Let’s break it down.

(This article is not intended to teach you in-depth concepts or provide even a basic functional coverage of the mathematical concepts needed for machine learning. Instead, it aims to discuss the topics you should explore further to develop the required mathematical skills for machine learning.)

Linear Algebra: The Bedrock of Data

Think of linear algebra as the ultimate organizational tool for data. Whether it’s images, sound, or just rows and columns of numbers, machine learning models perceive everything as vectors and matrices.

Here’s where linear algebra comes in:

• Matrices and Vectors: They are how data gets stored and processed.
• Matrix Operations: Multiplying matrices or breaking them down into smaller components forms the backbone of algorithms like PCA, which simplifies big datasets.
• Eigenvalues and Eigenvectors: These are critical for tasks like compressing data while preserving what is important.

In short, if you can handle rows and columns of numbers, you’re already halfway there.

Calculus: Making Machines Learn

When people talk about “training” machine learning models, they are really talking about calculus.

Here’s the gist. Machine learning models aim to minimize their error (or loss). Calculus helps determine how to tweak the model’s parameters, which are the magical numbers inside the algorithm, so it performs better.

How?

• Gradients: These indicate the steepest direction to reduce error.
• The Chain Rule: This drives backpropagation, which is the engine of neural networks.
• Optimization: Algorithms like Gradient Descent use calculus to hone in on the best solution.

If you’ve ever plotted a curve and wondered, What’s the steepest point here?, congratulations. You have touched on machine learning math.

Probability and Statistics: Dealing with Uncertainty

Machine learning isn’t perfect. It is all about making educated guesses. That’s where probability and statistics come in.

Here’s why they matter:

• Probability Distributions: These describe how likely things are to happen. For example, is this email spam or not?
• Bayes' Theorem: This is like the secret sauce behind spam filters and recommendation systems.
• Variance and Expectation: These help models account for randomness in real-world data.

Machine learning is all about taking what you know, combining it with what you don’t, and making the best prediction possible.

Optimization: Finding the Sweet Spot

Training a machine learning model is like tuning a guitar. You’re trying to strike the perfect balance between overthinking the problem (overfitting) and not thinking hard enough (underfitting). Optimization makes this possible.

Some key ideas:

• Convex Functions: These represent problems with a single, clear solution, which is ideal for machine learning.
• Gradient Descent Variants: Stochastic Gradient Descent, Adam, and others are advanced techniques to speed up the tuning process.
• Regularization: This prevents models from overcomplicating things, keeping them practical for real-world use.

A Bit of Geometry and Logic

Ever wonder how a computer “sees” things? Geometry plays a significant role. For example:

• Distance Metrics: These measure how similar (or different) two things are.
• Hyperplanes: These separate data into groups, such as determining whether a picture contains a cat or a dog.

Meanwhile, logic-based concepts from discrete math power decision trees and other rule-based models.

Why This Math Matters

So, why should you care about all this math? Because it is the key to understanding why machine learning works and how to make it work better. Without it, you’re stuck treating machine learning like a black box. With it, you can open the box, tweak things, and build something amazing.

Whether you’re just curious about how your favorite tech works or you’re planning to dive into machine learning yourself, these mathematical essentials are your first step into a world that is as exciting as it is transformative.

By Syed Faisal ur Rahman

CTO at Blockchain Laboratories and W3 SaaS Technologies Ltd.