[bhl]

For ML, you need both—probability to justify the setup of the problem, and linear algebra and calculus to optimize for a solution.

A simple example is with linear regression: find w such that the squared l2 norm of (Xw - y) is minimized.

Linear algebra will help with generalizing to n data points; and calculus will help with taking the gradient and setting equal to 0.

Probability will help with understanding why the squared l2 norm is an appropriate cost function; we assumed y = Xw + z, where z is Gaussian, and tried to maximize the likelihood of seeing y given x.

I’m sure there’s more examples of this duality since linear regression is one of the more basic topics in ML.