Learning about Learning - Part 1
The plan for the next few weeks is to develop a deep understanding about machine learning and statistics. Even though I have used and applied machine learning to many projects, and have taken a number of offline and online courses on machine learning, I feel like I don’t have a visceral understanding of it and have barely scratched the surface. My goal is to have a strong theoretical foundation and avoid the “throw things at it and see what sticks” approach.
Stage 1: Build a strong mathematical foundation, be able to reason about probability from a measure theoretic perspective and fill in holes in math. The plan of attack is:
- Learn real analysis by going through Francis Su’s Youtube lectures and using the following books as reference:
- Principles of Mathematical Analysis by Rudin
- Understanding Analysis by Abbott
- Real Mathematical Analysis by Pugh
- The next step is to do some abstract linear algebra, perhaps Linear Algebra Done Right by Axler. and follow it up by going through ODEs, PDEs and the calculus of variations in AD Aleksandrov’s Mathematics - Its Contents, Methods and Meaning.
- That should be enough background to learn about measure theory.
- A First Look at Rigorous Probability Theory by Rosenthal
- Real Analysis - Measure Theory, Integration and Hilbert Spaces by Stein
I will write more about Stage 2 in a future blog post and about tactics/lessons about effectively learning this material, provided I am able to get through it in a reasonable amount of time.