Toolkit revisited

I joined TTI Chicago almost a year ago, and it’s been an interesting time here. Since my background is a bit different from most of the other folks here, I have many moments of “academic cognitive dissonance” as it were — but more on that later. Madhur Tulsiani is going to offer a toolkit course in the spring focusing on mathematical tools for CS theory — I wanted to revisit a topic from a few years ago, namely what an EE-systems/theory “toolkit” would look like. I think a similar course / seminar would be really handy (even for self-study), but the topics we came up with before seem a little dated now. It seems like the topics fall under a few categories

• advanced stochastic processes : stochastic approximation
• mathematical economics : game theory, auctions, mechanism design
• advanced probability : concentration of measure, random graphs
• optimization : stochastic control, dynamic programming, convex optimization
• mathematical statistics : asymptotic statistics, minimax theory

Roy’s observation is that these topics are already covered in graduate syllabi is still apt. But I still think that knowing a smattering of these topics is still important for general literacy and critical reading of papers. In reading a new paper I first situate the techniques within the context of things I know about — if I have to absorb the author’s cursory description of the general method as well as its application to the problem at hand, I get bogged down in the former and find the latter mystifying.

Actually, I think what would be great is to make tutorials on the topics and gather them together. I know that people who make research tutorials spend a lot of time on them and there’s some reluctance to gather them together, but these topics are not bleeding edge and could be part of a course. It’s sort of like Connexions, but perhaps a little less wiki-like and more lecture-notes like. What would be the best way to do that?

As an aside, Madhur is also thinking of doing a more focused course later which would cover coding and information theory for (theoretical) computer scientists. I’ve thought a fair bit about such a course focused on machine learning — focusing a bit more on statistical issues like redundancy and Sanov’s theorem instead of Gaussian channels. But how could one do an information theory course without $\frac{1}{2} \log( 1 + \mathsf{SNR} )$?

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