One quick comment: in general it is a bad idea to compute the inverse of a matrix (to solve a linear system). It's much better to compute the QR factorization or SVD instead (or simply call least square solver). See for example: https://www.johndcook.com/blog/2010/01/19/dont-invert-that-m...
Thank you for the feedback. :) I plan on fixing this soon!
Not very important and for a learning project I find using cvxpy a better idea as it's more readable ( like you did ) but:
Solving the full quadratic optimization problem for SVMs in basically impossible to do. You are forming an n^2 matrix, so I'm going to let you imagine what happens when n = 100 000.
Using people use either approximation methods ( Incomplete Cholesky, Nystrom ) or do it exactly but iteratively ( SMO, Pegasos... )
I'm implementing them for class right now so it's still fresh in my head haha