Interdisciplinary PhD in Statistics (Stats+Math+CS+Physics+Engineering) at the University of Wisconsin - Madison
Special emphasis on Mathematics and Computer Science (double Minor) to support the development of Machine Learning theory.
Tentative credit breakdown:
- Stats: 33%
- Math: 28%
- CS: 25%
- Physics: 7%
- Engineering: 7%
Gratefully funded 100% by the "la Caixa" Foundation and the Department of Statistics at UW-Madison.
Research areas:
- Explainable AI
- Risk Management, Financial Time Series
Designing my own curriculum of classes to deliver optimal preparation to do first-rate research in the areas above with an almost unfair advantage.
Fall '19
* Physics 208 (Calculus Physics II: Electromagnetism, waves, optics, relativity & quantum physics) [Accelerated class, 2-course equivalent]
Spring '20
* Math 341 (Linear Algebra: Proof-based, Honors version of Strang's 18.06 MIT class)
Summer '20
* CS 524 (Intro to discrete & continuous Optimization)
Special emphasis on Mathematics and Computer Science (double Minor) to support the development of Machine Learning theory.
Tentative credit breakdown:
- Stats: 33%
- Math: 28%
- CS: 25%
- Physics: 7%
- Engineering: 7%
Gratefully funded 100% by the "la Caixa" Foundation and the Department of Statistics at UW-Madison.
Research areas:
- Explainable AI
- Risk Management, Financial Time Series
Designing my own curriculum of classes to deliver optimal preparation to do first-rate research in the areas above with an almost unfair advantage.
Fall '19
* Physics 208 (Calculus Physics II: Electromagnetism, waves, optics, relativity & quantum physics) [Accelerated class, 2-course equivalent]
- Goals: 1) To gain an insight into a the mind of a Physicist. 2) Learn a fascinating subject I had not studied in 15 years. 3) Complement my STEM studies
- Outcomes: 1) Learnt the more geometric and practical way of thinking of Physicists vs Mathematicians. 2) Learnt immensely, and have been blown away by Modern Physics (Special Relativity: you can travel into the future if you move fast enough, General Relativity: gravity is an illusion (mass curves space in a 4th dimension), Quantum Physics: everything, humans included, is both a particle and a wave). 3) Sharpened my knowledge on geometry/trigonometry and waves + different thinking approach
- Goals: 1) To review key material for my PhD. 2) Get back into the abstract math mindset
- Outcomes: 1) and 2) achieved
Spring '20
* Math 341 (Linear Algebra: Proof-based, Honors version of Strang's 18.06 MIT class)
- Goals: 1) To review / solidify key material for my PhD. 2) Gain proof experience in an area that I currently don't have enough
- Outcomes: 1) Not only that but also learnt new stuff! Say 1/5 of the material was truly new to me, which is way more than I anticipated. 2) At a rate of around 7 proof-based problems per week for 11 weeks + 2 midterms and 1 final, I got 100+ linear algebra proofs under my belt now
- Goals: To continue to deepen my analysis knowledge and general math maturity
- Outcome: The most challenging class of the semester by far, and probably in my top 3 thoughest classes I've ever taken. Took a lot but gave back a lot too. Now pretty much anything in undergrad math seems "easy" or at least doable. We covered from approximation theory (including Fourier analysis), to differentiation in abstract normed vector spaces, to some theory on ODE's. All this with elements of functional analysis all along.
- Goals: 1) To acquire essential knowledge for certain ML approaches like Topological Data Analysis. 2) Work on this currently weak supporting area of Math that will unlock great potential in more directly relevant areas to my PhD
- Outcomes: Although I do not feel I have by any means an advanced knowledge of Topology (not even at undergrad level), I have learnt the basics well, and I believe this is enough for my purposes! 2) I feel my abstract math background has got a significant boost after learning basic topology, and feel much less intimidated by the topology bits one encounters in analysis, advanced probability theory/mathematical statistics, and optimization, as well as I suspect (theoretical) machine learning.
Summer '20
* CS 524 (Intro to discrete & continuous Optimization)
- Goals: 1) To review / solidify key material for my PhD. 2) To beef up my knowledge of discrete optimization, which is at the moment much weaker than my continous conterpart.
- Goals: To review / solidify key material on my primary area of research, from a more AI as opposed to "statistical learning" perspective