Maths for Machine Learning

About this track

Almost every machine learning explanation stops to say "recall that the gradient points uphill" or "this is just a dot product" and moves on. This track is where you go to actually see those things, one at a time, with something you can drag.

It starts at the equation of a line and works up through vectors, matrix multiplication, derivatives and probability distributions. Nothing here assumes a maths degree, and nothing is left as an exercise for the reader.

The order matters more here than anywhere else on the site. Each page is built only from ideas introduced before it, so the track can be read straight through without ever hitting a symbol that has not been explained.

What you will be able to do

• Read a vector as both a list of numbers and a direction, and say what a dot product measures.
• Multiply matrices by hand, and explain why the inner dimensions have to agree.
• Interpret a derivative as a slope and a gradient as the direction of steepest increase.
• Tell a probability distribution from a likelihood, and read what a standard deviation claims.
• Recognise these objects when they appear unannounced in a machine learning paper.

How the track is ordered

Start at the equation of a line, because every later idea is a generalisation of it: a slope becomes a gradient, a line becomes a plane, and a coefficient becomes a weight. From there the track splits into three strands that meet at the end - linear algebra (vectors, dot products, matrices as transformations), calculus (derivatives, partial derivatives, the chain rule), and probability (distributions, expectation, Bayes). Nothing assumes a maths degree. If you can rearrange an equation and read a graph, you have the prerequisites.

Where this leads

Once the gradient and the dot product are familiar, the machine learning and deep learning tracks stop being notation and start being mechanisms. Gradient descent is a derivative followed downhill; a neuron is a dot product with a bias. Most people find those tracks considerably easier after this one, which is why it is first on the learning path.