Learning Math for Machine Learning

Vincent Chen is a student at Stanford University studying Computer Science. He is also a Research Assistant at the Stanford AI Lab.

It’s not entirely clear what level of mathematics is necessary to get started in machine learning, especially for those who didn’t study math or statistics in school.

In this piece, my goal is to suggest the mathematical background necessary to build products or conduct academic research in machine learning. These suggestions are derived from conversations with machine learning engineers, researchers, and educators, as well as my own experiences in both machine learning research and industry roles.

To frame the math prerequisites, I first propose different mindsets and strategies for approaching your math education outside of traditional classroom settings. Then, I outline the specific backgrounds necessary for different kinds of machine learning work, as these subjects range from high school-level statistics and calculus to the latest developments in probabilistic graphical models (PGMs). By the end of the post, my hope is that you’ll have a sense of the math education you’ll need to be effective in your machine learning work, whatever that may be!

To preface the piece, I acknowledge that learning styles/frameworks/resources are unique to a learner’s personal needs/goals— your opinions would be appreciated in the discussion on HN!

A Note on Math Anxiety
It turns out that a lot of people — including engineers — are scared of math. To begin, I want to address the myth of “being good at math.”

The truth is, people who are good at math have lots of practice doing math. As a result, they’re comfortable being stuck while doing math. A student’s mindset, as opposed to innate ability, is the primary predictor of one’s ability to learn math (as shown by recent studies).

To be clear, it will take time and effort to achieve this state of comfort, but it’s certainly not something you’re born with. The rest of this post will help you figure out what level of mathematical foundation you need and outline strategies for building it.


8 logical fallacies that are hard to spot

  • A fallacy is the use of invalid or faulty reasoning in an argument.
  • There are two broad types of logical fallacies: formal and informal.
  • A formal fallacy describes a flaw in the construction of a deductive argument, while an informal fallacy describes an error in reasoning.

In arguments, few things are more frustrating than when you realize that someone is using bad logic, but you can’t quite identify what the problem is.

This rarely happens with the more well-known logical fallacies. For example, when someone in an argument starts criticizing the other person’s reputation instead of their ideas, most people know that’s an ad hominem attack. Or, when someone compares two things to support their argument, but it doesn’t make sense, that’s a false equivalency. But other fallacies are harder to spot. For example, say you’re arguing about politics with a friend, and they say:

“The far-left is crazy. The far-right is violent. That’s why the right answers lie the middle.”

Sure, it might be true that moderation is the answer. But just because two extremes exist doesn’t mean that the truth necessarily lies between those extremes. Put more starkly: If one person says the sky is blue, but someone else says it’s yellow, that doesn’t mean the sky is green. This is an argument to moderation, or the middle ground fallacy — you hear it a lot from people who are trying to mediate conflicts.

When you find yourself in arguments, it’s valuable to be able to spot and, if necessary, call out logical fallacies like this. It can protect you against bad ideas. Check out a few more examples of logical fallacies that can be tough to spot…