bencw

> I am uncertain why this is such a travesty

> If a school is willing to accept sub-par students then they will see their own stats decline

I think you just answered your own question.

You'd have to file taxes, but won't necessarily owe any.

I think it's a play on "Any sufficiently advanced technology is indistinguishable from magic".

I see what you're getting at with the first point but what about the second? It seems to me the "quality of engineering culture" at a company doesn't need to correlate with company size.

This is something I've wondered about (along with potential applications of autograd outside of deep learning). Do you have a recommended starting point for someone who wants to learn more about this?

This comparison holds true for most major European nations vs the US.

This is a general fact about Gibbs distributions!

Why is this? Is there a brain drain going on?

This book is great and very much complementary to Strang's approach in that it leans more towards "abstract" linear algebra.

This is very well put. Knowledge has a hierarchical (or perhaps even cyclical!) structure and it's unrealistic to think that a body of knowledge can be taught or learned sequentially.

Maybe I'm biased, but I really don't think so. Monads are quite a bit more abstract than the concepts in linear algebra. Linear algebra is both geometric and algorithmic and therefore very intuitive. Most of the difficulty people have learning linear algebra can be attributed to poor teaching methods.

Honestly, I think working with computers (possibly some programming) should be more frequently integrated into math courses. A computer is a natural to really interact with the material, like labs in the natural sciences. We're lucky to live in a time where this is possible, but sadly math education is taking it's sweet time taking advantage of this possibility.

A common type of example involves relatively small or uninformative datasets. Say you flip a coin a few times and only get heads. Your maximum likelihood (frequentist) estimate is that the coin will always land heads. In a Bayesian setting, if you have a (say uniform) prior on the probability that the coin lands heads, your maximum a posteriori estimate of this probability will be non-zero, but will get continue to get smaller if you continue only seeing heads.

The above example is contrived, but makes more sense in the case of language modelling. Since a bag-of-words vector, containing say counts of words seen in a document, is typically sparse (most documents only contain a limited portion of the full vocabulary), a frequentist estimate of word probability will say that certain words can never occur, just because it's never seen them. The Bayesian estimate will still assign some non-zero chance of seeing that word.

Practically speaking, this leads to the idea of "smoothing" in tf-idf (text-frequency-inverse-document-frequency) vectors, by adding 1 to document frequencies. You don't need Bayesian statistics to do this, but maybe you never would have thought of it otherwise!

I find this statement from Paul Graham's Revenge of the Nerds enlightening:

> Lisp looks strange not so much because it has a strange syntax as because it has no syntax; you express programs directly in the parse trees that get built behind the scenes when other languages are parsed, and these trees are made of lists, which are Lisp data structures.